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g3pA_taskc.txt vs g3pB_taskd.txt

Vector space model, or term vector model as it is also known, is an algebraic model for representing objects (although it is mainly used for text documents) as vectors of identifiers; for example, index terms. It is used in information retrieval and filtering, indexing and relevancy rankings, and was first used in the SMART Information Retrieval System.

A document is represented as a vector, with each dimension corresponding to a separate term. If a term occurs in the document, the value will be non-zero in the vector. Many different ways of computing these values (aka (term) weights) have been developed; one of the best known schemes is tf-idf weighting.

The way that a 'term' is defined depends on the application. Typically, terms are single words, keywords, or sometimes even longer phrases. If the words are chosen as the terms, the number of dimensions in the vector is the number of distinct words in the corpus.

Relevancy ranks for documents, in a keyword search, can be calculated; this uses the assumptions of document similarities theory, by comparing the difference of angles between each document vector and the original query vector, where the query is represented as same format vector as the documents.

Generally, it is easier to calculate the cosine of the angle between the vectors instead of the angle itself. A zero value for the cosine indicates that the query and document vector are orthogonal and so had no match; this means the query term did not exist in the document being considered.

However, the vector space model has limitations. Long documents are poorly represented due to their poor similarity values (a small scalar product and a large dimensionality); search keywords must match precisely the document terms; word substrings might result in a "false positive match"; similar context documents but different term vocabulary won't be associated, leading to a "false negative match"; and the order that the terms appear in the document is not represented in the vector space model.

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

g3pA_taskc.txt vs g3pC_taskd.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

g3pA_taskc.txt vs g4pD_taskb.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

g3pA_taskc.txt vs g0pA_taska.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

g3pA_taskc.txt vs g0pB_taskb.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

g3pA_taskc.txt vs g1pA_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

g3pA_taskc.txt vs g2pA_taske.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

g3pA_taskc.txt vs g4pE_taska.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

g3pA_taskc.txt vs g0pA_taskd.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

g3pA_taskc.txt vs g0pC_taskc.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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g3pA_taskc.txt vs g1pB_taskd.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

g3pA_taskc.txt vs g4pB_taskc.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

g3pA_taskc.txt vs g2pC_taskb.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

g3pA_taskc.txt vs g3pB_taskb.txt

PageRank is an algorithm that was developed by Google to provide the most relevant search results to its users queries. PageRank, along with similar algorithms developed by Google’s competitors for their search engines, is part of the second generation of technologies designed to rate the importance of web pages: the first, which was solely based on keywords in the page content and meta-data, could easily be influenced by those wishing to obtain a higher ranking for their less-relevant pages.

The different with PageRank is that it tries to determine a web page’s relevance to users by attempting to determine its importance. It does this by assigning it a value of importance that is dependant upon the number of web sites that link to that page, taking into account the importance value, or PageRank, of those pages. The PageRank is computed iteratively, and it is found that the PageRank values converge fairly rapidly.

Although it is much better than simple keyword-based ranking algorithms, PageRank is not infallible: we have an internet where advertising revenue can make up most - and quite frequently all – of a web site’s income and the people that run these web sites will always be trying to trick the system into giving their pages a higher PageRank. One of Google’s attempts to counter this is their Google Toolbar browser plugin.

Google Toolbar is a free tool which provides a number of useful functions in a convenient location: the users web browser window. Google’s payoff is that it gets to track the behaviour of actual users. This allows them to see whether their PageRank algorithm is accurate in assigning high PageRank values to the most relevant web pages and, just as importantly, low values to those that are irrelevant and try to fool the system.

g3pA_taskc.txt vs g3pB_taske.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

g3pA_taskc.txt vs g3pC_taskb.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

g3pA_taskc.txt vs g0pE_taske.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

g3pA_taskc.txt vs g1pB_taska.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

g3pA_taskc.txt vs g1pD_taskd.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

g3pA_taskc.txt vs g2pA_taskd.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation.
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications.
Suppose there is a co-ed school having 60% boys and 40% girls as students. The girl students wear trousers or skirts in equal numbers; the boys all wear trousers. An observer sees a (random) student from a distance; all they can see is that this student is wearing trousers. What is the probability this student is a girl? The correct answer can be computed using Bayes' theorem.
The event A is that the student observed is a girl, and the event B is that the student observed is wearing trousers. To compute P(A|B), we first need to know:
P(B|A'), or the probability of the student wearing trousers given that the student is a boy. This is given as 1.
P(A), or the probability that the student is a girl regardless of any other information. Since the observers sees a random student, meaning that all students have the same probability of being observed, and the fraction of girls among the students is 40%, this probability equals 0.4.
P(A'), or the probability that the student is a boy regardless of any other information (A' is the complementary event to A). This is 60%, or 0.6.
P(B|A), or the probability of the student wearing trousers given that the student is a girl. As they are as likely to wear skirts as trousers, this is 0.5

g3pA_taskc.txt vs g3pC_taske.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

g3pA_taskc.txt vs g4pB_taskb.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

g3pA_taskc.txt vs g4pE_taske.txt

Dynamic programming is a method for efficiently solving a broad range of search and optimization problems which exhibit the characteristics of overlappling. Dynamic programming. Design technique, like divide-and-conquer method.

The leading and most up-to-date textbook on the far-ranging algorithmic methododogy of Dynamic Programming, which can be used for optimal control, ...
The word Programming in the name has nothing to do with writing computer programs. Mathematicians use the word to describe a set of rules which anyone can follow to solve a problem. They do not have to be written in a computer language.
Dynamic programming was the brainchild of an American Mathematician, Richard Bellman, who described the way of solving problems where you need to find the best decisions one after another. In the forty-odd years since this development, the number of uses and applications of dynamic programming has increased enormously.
For example, in 1982 David Kohler used dynamic programming to analyse the best way to play the game of darts.

1. In recent years, dynamic programming languages develope very fastly, especially PHP and Ruby. There is no doubt that They have already became the first choice for many programmerers when developing web applications..When you learn a new natural language and you start to use it you naturally, you find yourself using new concepts and paradigms that enrich the use of the language you already know; expect the same result with computer languages.

g3pA_taskc.txt vs g1pD_taskb.txt

g3pA_taskc.txt vs g3pC_taska.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

g3pA_taskc.txt vs g4pD_taskc.txt

In vector space model, the documents from which the information is to be retrieved are represented as vectors. The term weighting indentifies the success or failure of the vector space method. Terms are basically the words or any indexing unit used to identify the contents of a text. Furthermore, a term weighting scheme plays an important role for the similarity measure. The similarity measures largely identify the retrieval efficiency of a particular information retrieval system.
This largely depends on formulas. Where the formulas depend only on the frequencies within the document and they not depend on inter-document frequencies. The main components of the formulas are as follows:
Binary:
Binary formula gives every word that appears in a document equal relevance. This can be useful when the number of times a word appears is not considered important.
Term frequency:
This formula counts how many times the term occurs in a document. The more times a term t occurs in document d the more likely it is that t is relevant to the document. Used alone, favors common words and long documents. This formula gives more credit to words that appears more frequently, but often too much credit.
Augmented normalized term frequency
This formula tries to give credit to any word that appears and then give some additional credit to words that appear frequently.
Logarithmic term frequency
Logarithms are a way to de-emphasize the e_ect of frequency. Literature proposes log and alternate log as the most used

g3pA_taskc.txt vs g4pE_taskb.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
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g3pA_taskc.txt vs g0pB_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g3pA_taskc.txt vs g1pA_taska.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g3pA_taskc.txt vs g1pA_taske.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g3pA_taskc.txt vs g4pB_taske.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem. In general, we can solve a problem with optimal substructure using a three-step process:

1. Break the problem into smaller subproblems.
2. Solve these problems optimally using this three-step process recursively.
3. Use these optimal solutions to construct an optimal solution for the original problem.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems. For example, in the Fibonacci sequence, F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. This applies whenever overlapping subproblems are present: a naive approach may waste time recomputing optimal solutions to subproblems it has already solved.

In order to avoid this, we instead save the solutions to problems we have already solved. Then, if we need to solve the same problem later, we can retrieve and reuse our already-computed solution. If we are sure we won't need a particular solution anymore, we can throw it away to save space. In some cases, we can even compute the solutions to subproblems we know that we'll need in advance.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g3pA_taskc.txt vs g2pE_taskd.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g3pA_taskc.txt vs g4pB_taska.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g3pA_taskc.txt vs g4pB_taskd.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g3pA_taskc.txt vs g4pC_taskc.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g3pA_taskc.txt vs g0pE_taskb.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g3pA_taskc.txt vs g1pD_taske.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g3pA_taskc.txt vs g2pB_taskb.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g3pA_taskc.txt vs g2pB_taskd.txt

In probability theory, Bayes' theorem also called Bayes' law after Rev Thomas Bayes compares the conditional and marginal probabilities of two random events. It is often used to calculate posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to calculate the likelihood that a proposed analysis is accurate, given that observation.
As an official theorem, Bayes' theorem is valid in all universal interpretations of probability. However, it plays a fundamental role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications.
Frequentists assign probabilities to random events according to their frequencies of happening or to subsets of populations as proportions of the whole. Whilst Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem compares the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability.
Each term in Bayes' theorem has a conventional name:
P(A) is the previous probability of A. It is "previous" in the sense that it does not take into account any information about B.
P(A|B) is the conditional probability of A, given B. It is also called the subsequent probability because it is derived from or depends upon the specified value of B.
P(B|A) is the conditional probability of B given A.
P(B) is the previous.

g3pA_taskc.txt vs g3pA_taske.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g3pA_taskc.txt vs g4pC_taskd.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is usually be used to compute posterior probabilities given observations. For instance, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation.
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole. At the same time, Bayesians describe probabilities in terms of beliefs and degrees of uncertainty.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
Each term in Bayes' theorem has a conventional name:
• P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
• P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
• P(B|A) is the conditional probability of B given A.
• P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g3pA_taskc.txt vs orig_taskb.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. The university received 1.8 million shares in Google in exchange for use of the patent; the shares were sold in 2005 for $336 million.
Google describes PageRank:
“ PageRank relies on the uniquely democratic nature of the web by using its vast link structure as an indicator of an individual page's value. In essence, Google interprets a link from page A to page B as a vote, by page A, for page B. But, Google looks at more than the sheer volume of votes, or links a page receives; it also analyzes the page that casts the vote. Votes cast by pages that are themselves "important" weigh more heavily and help to make other pages "important". ”
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). A page that is linked to by many pages with high PageRank receives a high rank itself. If there are no links to a web page there is no support for that page.
Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank denotes a site’s importance in the eyes of Google. The PageRank is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank of a particular page is roughly based upon the quantity of inbound links as well as the PageRank of the pages providing the links. It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank. In order to prevent manipulation, spoofing and Spamdexing, Google provides no specific details about how other factors influence PageRank.
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper. In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank.
Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank algorithm.

g3pA_taskc.txt vs g0pE_taskc.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g3pA_taskc.txt vs g2pB_taskc.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g3pA_taskc.txt vs g2pC_taske.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g3pA_taskc.txt vs g3pA_taskd.txt

As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics; frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Each term in Bayes' theorem has a conventional name:
P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
P(B|A) is the conditional probability of B given A.
P(B) is the prior or marginal probability of B, and acts as a normalizing constant.

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g3pA_taskc.txt vs g1pA_taskc.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g3pA_taskc.txt vs g3pA_taskb.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g3pA_taskc.txt vs orig_taska.txt

The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization (what is known about specific entities is applied to a wider group given a belongs relation can be established) and cognitive economy (less information needs to be stored about each specific entity, only its particularities).

Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g3pA_taskc.txt vs orig_taskd.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g3pA_taskc.txt vs g0pA_taskb.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g3pA_taskc.txt vs g0pB_taske.txt

Dynamic programming is a method for solving mathematical programming problems that exhibit the properties of overlapping subproblems and optimal substructure. This is a much quicker method than other more naive methods. The word "programming" in "dynamic programming" relates optimization, which is commonly referred to as mathematical programming. Richard Bellman originally coined the term in the 1940s to describe a method for solving problems where one needs to find the best decisions one after another, and by 1953, he refined his method to the current modern meaning.

Optimal substructure means that by splitting the programming into optimal solutions of subproblems, these can then be used to find the optimal solutions of the overall problem. One example is the computing of the shortest path to a goal from a vertex in a graph. First, compute the shortest path to the goal from all adjacent vertices. Then, using this, the best overall path can be found, thereby demonstrating the dynamic programming principle. This general three-step process can be used to solve a problem:

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g3pA_taskc.txt vs g0pD_taskb.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g3pA_taskc.txt vs g0pD_taske.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g3pA_taskc.txt vs g3pB_taskc.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g3pA_taskc.txt vs g3pC_taskc.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g3pA_taskc.txt vs g4pC_taskb.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g3pA_taskc.txt vs g4pC_taske.txt

In mathematics and computer science, dynamic programming is a methodology of the solution of the problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The methodology takes much less time rather than naive methods.
The term was originally used during the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programmer, which restates an optimization problem in recursive form.
The word "programming" in "dynamic programming" has no particular connection to computer programming in general , and instead of this it comes from the term "mathematical programming", a synonym for optimization. Therefore, the "program" is the optimal plan for action that is produced. For example, a finalized schedule of events at an exhibition is sometimes called a program.
Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem. For instance, the shortest path to a goal from a vertex in a graph can be found by first computing the shortest path to the goal from all adjacent vertices. After this, it is using this to pick the best overall path. In a word, we can solve a problem with optimal substructure using a three-step process.

g3pA_taskc.txt vs g0pA_taske.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g3pA_taskc.txt vs g0pE_taska.txt

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula. The new classes, known as derived classes, take over (or inherit) attribute and behaviour of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification. Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization (what is known about specific entities is applied to a wider group given a belongs relation can be established) and cognitive economy (less information needs to be stored about each specific entity, only its particularities). Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant. An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code. Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

g3pA_taskc.txt vs g3pA_taska.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g3pA_taskc.txt vs g3pB_taska.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g3pA_taskc.txt vs g4pD_taska.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g3pA_taskc.txt vs orig_taskc.txt

Vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as, for example, index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. Its first use was in the SMART Information Retrieval System.
A document is represented as a vector. Each dimension corresponds to a separate term. If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, also known as (term) weights, have been developed. One of the best known schemes is tf-idf weighting (see the example below).
The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary (the number of distinct words occurring in the corpus).
The vector space model has the following limitations:
1. Long documents are poorly represented because they have poor similarity values (a small scalar product and a large dimensionality)
2. Search keywords must precisely match document terms; word substrings might result in a "false positive match"
3. Semantic sensitivity; documents with similar context but different term vocabulary won't be associated, resulting in a "false negative match".
4. The order in which the terms appear in the document is lost in the vector space representation.

g3pA_taskc.txt vs g0pA_taskc.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g3pA_taskc.txt vs g2pA_taska.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g3pA_taskc.txt vs g2pC_taskd.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g3pA_taskc.txt vs g4pD_taske.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g3pA_taskc.txt vs g4pD_taskd.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g3pA_taskc.txt vs g0pB_taska.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g3pA_taskc.txt vs g1pB_taske.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g3pA_taskc.txt vs g2pA_taskb.txt

The algorithm that Google uses to assign a weighting to each element of a linked set of documents, with the purpose of "measuring" its relative importance within the set.
A particular websites PageRank results from a "vote" from other pages on the Internet about how important that website actually is. A link to a page is seen as a vote of support. The PageRank depends on the PageRank rating and number of all pages that have links to it. Additionally, if a page is linked to by pages with a high PageRank rating, this increases the rating of the original page.
The PageRank scale ranges from 0-10. The rating of a certain page is generally based upon the quantity of inbound links as well as the perceived quality of the pages providing the links.
PageRank could be described as a probability distribution representing the chance that someone randomly clicking on links will reach a certain page. The PageRank calculations require iterations through the collection of web pages to alter approximate PageRank values to accurately reflect the actual rank.
In order to prevent spamming, Google releases little information on the way in which a PageRank is calculated. The PageRank algorithm has led to many sites being spammed with links in an attempt to artificially inflate the PageRank of the linked page, notably in blog comments and message boards. In 2005 a �nofollow� tag was added as an attribute of a HTML link to be used where Google shouldn�t change the PageRank of the linked page as a result of the link.

g3pA_taskc.txt vs g2pA_taskc.txt

A Vector space model (or term vector model) is an algebraic way of representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. Its first application was in the SMART Information Retrieval System.
A document can be represented as a vector. Every dimension relates to a different term. If a term appears in the document, the terms value in the vector is non-zero. Many different methods of calculating these values, sometimes known as (term) weights, have been developed. tf-idf weighting is one of the most well known schemes. (see below example).
The definition of a term depends on the application. Normally a term is a single word, keyword, or a longer phrase. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary (the number of distinct words occurring in the corpus).
The vector space model has some limitations:
1. Longer documents are represented poorly because the documents have poor similarity values (namely a small scalar product and a large dimensionality)
2. Search keywords have to precisely match document terms; word substrings could potentially result in a "false positive match"
3. Semantic sensitivity; documents with a similar context, but different term vocabulary won't be associated, resulting in a "false negative match".
4. The order in which terms appear in the document is lost in a vector space representation.

g3pA_taskc.txt vs g1pD_taska.txt

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g3pA_taskc.txt vs g2pB_taska.txt

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g3pA_taskc.txt vs g2pE_taskb.txt

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g3pA_taskc.txt vs g4pE_taskc.txt

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g3pA_taskc.txt vs g0pD_taskd.txt

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g3pA_taskc.txt vs g0pE_taskd.txt

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g3pA_taskc.txt vs g1pA_taskb.txt

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g3pA_taskc.txt vs g1pB_taskb.txt

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g3pA_taskc.txt vs g4pE_taskd.txt

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g3pA_taskc.txt vs g2pC_taska.txt

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g3pA_taskc.txt vs g2pC_taskc.txt

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g3pA_taskc.txt vs g2pE_taska.txt

When we talk about inheritance in object-oriented programming languages, which is a concept that was invented in 1967 for Simula, we are usually talking about a way to form new classes and classes are instances of which are called objects and involve using classes that have already been defined.
Derived classes are intended to help reuse existing code with little or no modification and are the new classes that take over (or inherit) attributes and behavior of the pre-existing classes, usually referred to as base classes (or ancestor classes).
Categorization in computer languages is a powerful way number of processing information and inheritance provides the support for representation by categorization. Furthermore, it is fundamental for helping humans learn by means of generalization in what is known about specific entities is applied to a wider group given a belongs relation can be established and cognitive processing which involves less information being acquired to be stored about each specific entity, but in actual fact only its particularities.
An instance of a "fruit" is a generalization of "apple", "orange", "mango" and many others. Inheritance can also sometimes be referred to as generalization, because is-a relationships represent a hierarchy amongst classes of objects. It can be considered that fruit is an abstraction of apple, orange, etc. Conversely, since apples are fruit, they may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
Modules with sufficiently similarities in interfaces would be able to share a lot of code and therefore reducing the complexity of the program. This can be known as one of the advantages of inheritance. Therefore inheritance can be known to have a further view, a dual, which describes many parts of code that are under control of shared control code, named as polymorphism.
On the other hand, inheritance is normally accomplished either by replacing one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor. A well known term used for this replacing act is called overriding.

g3pA_taskc.txt vs orig_taske.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods.
The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form.
The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem. For example, the shortest path to a goal from a vertex in a graph can be found by first computing the shortest path to the goal from all adjacent vertices, and then using this to pick the best overall path, as shown in Figure 1. In general, we can solve a problem with optimal substructure using a three-step process:
1. Break the problem into smaller subproblems.
2. Solve these problems optimally using this three-step process recursively.
3. Use these optimal solutions to construct an optimal solution for the original problem.
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Figure 2. The subproblem graph for the Fibonacci sequence. That it is not a tree but a DAG indicates overlapping subproblems.
To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems. For example, in the Fibonacci sequence, F3 = F1 + F2 and F4 = F2 + F3 — computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. This applies whenever overlapping subproblems are present: a naive approach may waste time recomputing optimal solutions to subproblems it has already solved.
In order to avoid this, we instead save the solutions to problems we have already solved. Then, if we need to solve the same problem later, we can retrieve and reuse our already-computed solution. This approach is called memoization (not memorization, although this term also fits). If we are sure we won't need a particular solution anymore, we can throw it away to save space. In some cases, we can even compute the solutions to subproblems we know that we'll need in advance.

g3pA_taskc.txt vs g0pB_taskc.txt

Vector space model is an algebraic model for representing text documents (and in general, any objects) as vectors of identifiers, such as, for example, index terms. Its first use was in the SMART Information Retrieval System. It is used in information filtering, information retrieval, indexing and relevancy rankings.

A document is represented as a vector, and each dimension corresponds to a separate term. If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, also known as (term) weights, have been developed. The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary (the number of distinct words occurring in the corpus).

One of the best known schemes is tf-idf weighting, proposed by Salton, Wong and Yang. In the classic vector space model, the term specific weights in the document vectors are products of local and global parameters.

Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.

The vector space model has the following limitations:

* Search keywords must precisely match document terms; word substrings might result in a "false positive match";
* Semantic sensitivity; documents with similar context but different term vocabulary won't be associated, resulting in a "false negative match";
* The order in which the terms appear in the document is lost in the vector space representation;
* Long documents are poorly represented because they have poor similarity values (a small scalar product and a large dimensionality).

g3pA_taskc.txt vs g0pC_taskd.txt

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g3pA_taskc.txt vs g0pC_taske.txt

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g3pA_taskc.txt vs g0pD_taskc.txt

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g3pA_taskc.txt vs g0pC_taskb.txt

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g3pA_taskc.txt vs g2pE_taske.txt

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g3pA_taskc.txt vs g0pC_taska.txt

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g3pA_taskc.txt vs g0pD_taska.txt

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g3pA_taskc.txt vs g4pC_taska.txt

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g3pA_taskc.txt vs g1pB_taskc.txt

The algebraic model for representing text documents and objects as vectors of identifiers is called the vector space model. It is used in information filtering, indexing, relevancy rankings and information retrieval. It was first used in the SMART Information Retrieval System.
When a document is represented as a vector, each dimension corresponds to a separate term. A term which occurs in the document has a value in the vector of non-zero. Other ways of computing these values, or weights, have been developed. The most popular is tf-idf weighting.
Depending on the application, the definition of term varies. Single words, keywords and occasionally longer phrases are used for terms. The dimensionality of the vector, if words are used as terms, is the total number of words available for use. By using the assumptions of the document similarities theory, the relevancy rankings of documents in a keyword search can be worked out by comparing the deviation of angles between vectors both within the document and the original query where the vectors of both are the same type.
The limitations of the vector space model are thus. Due to poor similarity values long documents are poorly represented. False positive matches may be returned if search keywords do not precisely match document terms. False negative matches could be returned when documents share a context but have different term vocabulary. Vector space representation results in the loss of the order which the terms are in the document.

g3pA_taskc.txt vs g1pD_taskc.txt

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g3pA_taskc.txt vs g2pB_taske.txt

In mathematics and computer science, dynamic programming is a method of solving problems, that exhibit the properties of overlapping subproblems and optimal substructure. The method takes much less time than naive methods.
The term was originally used in the 1940s to describe the process of solving problems where one needs to find the best decisions one after another.
The field was founded as a systems analysis and engineering topic that is recognized by the IEEE
The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem. For example, the shortest path to a goal from a vertex in a graph can be found by first computing the shortest path to the goal from all adjacent vertices, and then using this to pick the best overall path.
In general, we can solve a problem with optimal substructure using a three-step process:
1.Break the problem into smaller subproblems.
2.solve these problems optimally using this three-step process recursively.
3.Use these optimal solutions to construct an optimal solution for the original problem.
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

g3pA_taskc.txt vs g2pE_taskc.txt

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g3pB_taskd.txt vs g3pC_taskd.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

g3pB_taskd.txt vs g4pD_taskb.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

g3pB_taskd.txt vs g0pA_taska.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

g3pB_taskd.txt vs g0pB_taskb.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

g3pB_taskd.txt vs g1pA_taskd.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

g3pB_taskd.txt vs g2pA_taske.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

g3pB_taskd.txt vs g4pE_taska.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

g3pB_taskd.txt vs g0pA_taskd.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

g3pB_taskd.txt vs g0pC_taskc.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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g3pB_taskd.txt vs g1pB_taskd.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

g3pB_taskd.txt vs g4pB_taskc.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

g3pB_taskd.txt vs g2pC_taskb.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

g3pB_taskd.txt vs g3pB_taskb.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

g3pB_taskd.txt vs g3pB_taske.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

g3pB_taskd.txt vs g3pC_taskb.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

g3pB_taskd.txt vs g0pE_taske.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

g3pB_taskd.txt vs g1pB_taska.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

g3pB_taskd.txt vs g1pD_taskd.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

g3pB_taskd.txt vs g2pA_taskd.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

g3pB_taskd.txt vs g3pC_taske.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

g3pB_taskd.txt vs g4pB_taskb.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

g3pB_taskd.txt vs g4pE_taske.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

g3pB_taskd.txt vs g1pD_taskb.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

g3pB_taskd.txt vs g3pC_taska.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

g3pB_taskd.txt vs g4pD_taskc.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

g3pB_taskd.txt vs g4pE_taskb.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

g3pB_taskd.txt vs g0pB_taskd.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g3pB_taskd.txt vs g1pA_taska.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g3pB_taskd.txt vs g1pA_taske.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g3pB_taskd.txt vs g4pB_taske.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g3pB_taskd.txt vs g2pE_taskd.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g3pB_taskd.txt vs g4pB_taska.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g3pB_taskd.txt vs g4pB_taskd.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g3pB_taskd.txt vs g4pC_taskc.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g3pB_taskd.txt vs g0pE_taskb.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g3pB_taskd.txt vs g1pD_taske.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g3pB_taskd.txt vs g2pB_taskb.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g3pB_taskd.txt vs g2pB_taskd.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

g3pB_taskd.txt vs g3pA_taske.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g3pB_taskd.txt vs g4pC_taskd.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

g3pB_taskd.txt vs orig_taskb.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

g3pB_taskd.txt vs g0pE_taskc.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g3pB_taskd.txt vs g2pB_taskc.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g3pB_taskd.txt vs g2pC_taske.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g3pB_taskd.txt vs g3pA_taskd.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g3pB_taskd.txt vs g1pA_taskc.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g3pB_taskd.txt vs g3pA_taskb.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g3pB_taskd.txt vs orig_taska.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g3pB_taskd.txt vs orig_taskd.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g3pB_taskd.txt vs g0pA_taskb.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g3pB_taskd.txt vs g0pB_taske.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g3pB_taskd.txt vs g0pD_taskb.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g3pB_taskd.txt vs g0pD_taske.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g3pB_taskd.txt vs g3pB_taskc.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g3pB_taskd.txt vs g3pC_taskc.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g3pB_taskd.txt vs g4pC_taskb.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g3pB_taskd.txt vs g4pC_taske.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

g3pB_taskd.txt vs g0pA_taske.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g3pB_taskd.txt vs g0pE_taska.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

g3pB_taskd.txt vs g3pA_taska.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g3pB_taskd.txt vs g3pB_taska.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g3pB_taskd.txt vs g4pD_taska.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g3pB_taskd.txt vs orig_taskc.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

g3pB_taskd.txt vs g0pA_taskc.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g3pB_taskd.txt vs g2pA_taska.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g3pB_taskd.txt vs g2pC_taskd.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g3pB_taskd.txt vs g4pD_taske.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g3pB_taskd.txt vs g4pD_taskd.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g3pB_taskd.txt vs g0pB_taska.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g3pB_taskd.txt vs g1pB_taske.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g3pB_taskd.txt vs g2pA_taskb.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

g3pB_taskd.txt vs g2pA_taskc.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

g3pB_taskd.txt vs g1pD_taska.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g3pB_taskd.txt vs g2pB_taska.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g3pB_taskd.txt vs g2pE_taskb.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g3pB_taskd.txt vs g4pE_taskc.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g3pB_taskd.txt vs g0pD_taskd.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g3pB_taskd.txt vs g0pE_taskd.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g3pB_taskd.txt vs g1pA_taskb.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g3pB_taskd.txt vs g1pB_taskb.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g3pB_taskd.txt vs g4pE_taskd.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g3pB_taskd.txt vs g2pC_taska.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g3pB_taskd.txt vs g2pC_taskc.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g3pB_taskd.txt vs g2pE_taska.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

g3pB_taskd.txt vs orig_taske.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

g3pB_taskd.txt vs g0pB_taskc.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

The vector space model has the following limitations:

g3pB_taskd.txt vs g0pC_taskd.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g3pB_taskd.txt vs g0pC_taske.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g3pB_taskd.txt vs g0pD_taskc.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g3pB_taskd.txt vs g0pC_taskb.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g3pB_taskd.txt vs g2pE_taske.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g3pB_taskd.txt vs g0pC_taska.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g3pB_taskd.txt vs g0pD_taska.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g3pB_taskd.txt vs g4pC_taska.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g3pB_taskd.txt vs g1pB_taskc.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

g3pB_taskd.txt vs g1pD_taskc.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g3pB_taskd.txt vs g2pB_taske.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

g3pB_taskd.txt vs g2pE_taskc.txt

Bayes' theorem (often called Bayes' law) connects the conditional and marginal probabilities of two arbitrary events. One of its uses is calculating posterior probabilities given observations. 

Bayes' theorem plays a key role in the debate around the principles of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. 

Bayes' theorem is useful in evaluating the result of drug tests.  If a test can identify a drug user 99% of the time, and can identify a non-user as testing negative 99% of the time, it may seem to be a relatively accurate test.  However, Bayes' theorem will reveal the flaw that despite the apparently high accuracy of the test, the probability that an employee who tested positive actually did use drugs is only about 33%.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g3pC_taskd.txt vs g4pD_taskb.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

g3pC_taskd.txt vs g0pA_taska.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

g3pC_taskd.txt vs g0pB_taskb.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

g3pC_taskd.txt vs g1pA_taskd.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

g3pC_taskd.txt vs g2pA_taske.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

g3pC_taskd.txt vs g4pE_taska.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

g3pC_taskd.txt vs g0pA_taskd.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

g3pC_taskd.txt vs g0pC_taskc.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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g3pC_taskd.txt vs g1pB_taskd.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

g3pC_taskd.txt vs g4pB_taskc.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

g3pC_taskd.txt vs g2pC_taskb.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

g3pC_taskd.txt vs g3pB_taskb.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

g3pC_taskd.txt vs g3pB_taske.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

g3pC_taskd.txt vs g3pC_taskb.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

g3pC_taskd.txt vs g0pE_taske.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

g3pC_taskd.txt vs g1pB_taska.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

g3pC_taskd.txt vs g1pD_taskd.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

g3pC_taskd.txt vs g2pA_taskd.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

g3pC_taskd.txt vs g3pC_taske.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

g3pC_taskd.txt vs g4pB_taskb.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

g3pC_taskd.txt vs g4pE_taske.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

g3pC_taskd.txt vs g1pD_taskb.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

g3pC_taskd.txt vs g3pC_taska.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

g3pC_taskd.txt vs g4pD_taskc.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

g3pC_taskd.txt vs g4pE_taskb.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

g3pC_taskd.txt vs g0pB_taskd.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g3pC_taskd.txt vs g1pA_taska.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g3pC_taskd.txt vs g1pA_taske.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g3pC_taskd.txt vs g4pB_taske.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g3pC_taskd.txt vs g2pE_taskd.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g3pC_taskd.txt vs g4pB_taska.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g3pC_taskd.txt vs g4pB_taskd.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g3pC_taskd.txt vs g4pC_taskc.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g3pC_taskd.txt vs g0pE_taskb.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g3pC_taskd.txt vs g1pD_taske.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g3pC_taskd.txt vs g2pB_taskb.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g3pC_taskd.txt vs g2pB_taskd.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

g3pC_taskd.txt vs g3pA_taske.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g3pC_taskd.txt vs g4pC_taskd.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

g3pC_taskd.txt vs orig_taskb.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

g3pC_taskd.txt vs g0pE_taskc.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g3pC_taskd.txt vs g2pB_taskc.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g3pC_taskd.txt vs g2pC_taske.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g3pC_taskd.txt vs g3pA_taskd.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g3pC_taskd.txt vs g1pA_taskc.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g3pC_taskd.txt vs g3pA_taskb.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g3pC_taskd.txt vs orig_taska.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g3pC_taskd.txt vs orig_taskd.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g3pC_taskd.txt vs g0pA_taskb.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g3pC_taskd.txt vs g0pB_taske.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g3pC_taskd.txt vs g0pD_taskb.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g3pC_taskd.txt vs g0pD_taske.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g3pC_taskd.txt vs g3pB_taskc.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g3pC_taskd.txt vs g3pC_taskc.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g3pC_taskd.txt vs g4pC_taskb.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g3pC_taskd.txt vs g4pC_taske.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

g3pC_taskd.txt vs g0pA_taske.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g3pC_taskd.txt vs g0pE_taska.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

g3pC_taskd.txt vs g3pA_taska.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g3pC_taskd.txt vs g3pB_taska.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g3pC_taskd.txt vs g4pD_taska.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g3pC_taskd.txt vs orig_taskc.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

g3pC_taskd.txt vs g0pA_taskc.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g3pC_taskd.txt vs g2pA_taska.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g3pC_taskd.txt vs g2pC_taskd.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g3pC_taskd.txt vs g4pD_taske.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g3pC_taskd.txt vs g4pD_taskd.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g3pC_taskd.txt vs g0pB_taska.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g3pC_taskd.txt vs g1pB_taske.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g3pC_taskd.txt vs g2pA_taskb.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

g3pC_taskd.txt vs g2pA_taskc.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

g3pC_taskd.txt vs g1pD_taska.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g3pC_taskd.txt vs g2pB_taska.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g3pC_taskd.txt vs g2pE_taskb.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g3pC_taskd.txt vs g4pE_taskc.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g3pC_taskd.txt vs g0pD_taskd.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g3pC_taskd.txt vs g0pE_taskd.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g3pC_taskd.txt vs g1pA_taskb.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g3pC_taskd.txt vs g1pB_taskb.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g3pC_taskd.txt vs g4pE_taskd.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g3pC_taskd.txt vs g2pC_taska.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g3pC_taskd.txt vs g2pC_taskc.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g3pC_taskd.txt vs g2pE_taska.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

g3pC_taskd.txt vs orig_taske.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

g3pC_taskd.txt vs g0pB_taskc.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

The vector space model has the following limitations:

g3pC_taskd.txt vs g0pC_taskd.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g3pC_taskd.txt vs g0pC_taske.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g3pC_taskd.txt vs g0pD_taskc.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g3pC_taskd.txt vs g0pC_taskb.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g3pC_taskd.txt vs g2pE_taske.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g3pC_taskd.txt vs g0pC_taska.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g3pC_taskd.txt vs g0pD_taska.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g3pC_taskd.txt vs g4pC_taska.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g3pC_taskd.txt vs g1pB_taskc.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

g3pC_taskd.txt vs g1pD_taskc.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g3pC_taskd.txt vs g2pB_taske.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

g3pC_taskd.txt vs g2pE_taskc.txt

In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g4pD_taskb.txt vs g0pA_taska.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

g4pD_taskb.txt vs g0pB_taskb.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

g4pD_taskb.txt vs g1pA_taskd.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

g4pD_taskb.txt vs g2pA_taske.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

g4pD_taskb.txt vs g4pE_taska.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

g4pD_taskb.txt vs g0pA_taskd.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

g4pD_taskb.txt vs g0pC_taskc.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

g4pD_taskb.txt vs g1pB_taskd.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

g4pD_taskb.txt vs g4pB_taskc.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

g4pD_taskb.txt vs g2pC_taskb.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

g4pD_taskb.txt vs g3pB_taskb.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

g4pD_taskb.txt vs g3pB_taske.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

g4pD_taskb.txt vs g3pC_taskb.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

g4pD_taskb.txt vs g0pE_taske.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

g4pD_taskb.txt vs g1pB_taska.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

g4pD_taskb.txt vs g1pD_taskd.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

g4pD_taskb.txt vs g2pA_taskd.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

g4pD_taskb.txt vs g3pC_taske.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

g4pD_taskb.txt vs g4pB_taskb.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

g4pD_taskb.txt vs g4pE_taske.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

g4pD_taskb.txt vs g1pD_taskb.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

g4pD_taskb.txt vs g3pC_taska.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

g4pD_taskb.txt vs g4pD_taskc.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

g4pD_taskb.txt vs g4pE_taskb.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

g4pD_taskb.txt vs g0pB_taskd.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g4pD_taskb.txt vs g1pA_taska.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g4pD_taskb.txt vs g1pA_taske.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g4pD_taskb.txt vs g4pB_taske.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g4pD_taskb.txt vs g2pE_taskd.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g4pD_taskb.txt vs g4pB_taska.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g4pD_taskb.txt vs g4pB_taskd.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g4pD_taskb.txt vs g4pC_taskc.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g4pD_taskb.txt vs g0pE_taskb.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g4pD_taskb.txt vs g1pD_taske.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g4pD_taskb.txt vs g2pB_taskb.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g4pD_taskb.txt vs g2pB_taskd.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

g4pD_taskb.txt vs g3pA_taske.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g4pD_taskb.txt vs g4pC_taskd.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

g4pD_taskb.txt vs orig_taskb.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

g4pD_taskb.txt vs g0pE_taskc.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g4pD_taskb.txt vs g2pB_taskc.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g4pD_taskb.txt vs g2pC_taske.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g4pD_taskb.txt vs g3pA_taskd.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g4pD_taskb.txt vs g1pA_taskc.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g4pD_taskb.txt vs g3pA_taskb.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g4pD_taskb.txt vs orig_taska.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g4pD_taskb.txt vs orig_taskd.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g4pD_taskb.txt vs g0pA_taskb.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g4pD_taskb.txt vs g0pB_taske.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g4pD_taskb.txt vs g0pD_taskb.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g4pD_taskb.txt vs g0pD_taske.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g4pD_taskb.txt vs g3pB_taskc.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g4pD_taskb.txt vs g3pC_taskc.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g4pD_taskb.txt vs g4pC_taskb.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g4pD_taskb.txt vs g4pC_taske.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

g4pD_taskb.txt vs g0pA_taske.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g4pD_taskb.txt vs g0pE_taska.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

g4pD_taskb.txt vs g3pA_taska.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g4pD_taskb.txt vs g3pB_taska.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g4pD_taskb.txt vs g4pD_taska.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g4pD_taskb.txt vs orig_taskc.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

g4pD_taskb.txt vs g0pA_taskc.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g4pD_taskb.txt vs g2pA_taska.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g4pD_taskb.txt vs g2pC_taskd.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g4pD_taskb.txt vs g4pD_taske.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g4pD_taskb.txt vs g4pD_taskd.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g4pD_taskb.txt vs g0pB_taska.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g4pD_taskb.txt vs g1pB_taske.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g4pD_taskb.txt vs g2pA_taskb.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

g4pD_taskb.txt vs g2pA_taskc.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

g4pD_taskb.txt vs g1pD_taska.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g4pD_taskb.txt vs g2pB_taska.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g4pD_taskb.txt vs g2pE_taskb.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g4pD_taskb.txt vs g4pE_taskc.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g4pD_taskb.txt vs g0pD_taskd.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g4pD_taskb.txt vs g0pE_taskd.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g4pD_taskb.txt vs g1pA_taskb.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g4pD_taskb.txt vs g1pB_taskb.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g4pD_taskb.txt vs g4pE_taskd.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g4pD_taskb.txt vs g2pC_taska.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g4pD_taskb.txt vs g2pC_taskc.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g4pD_taskb.txt vs g2pE_taska.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

g4pD_taskb.txt vs orig_taske.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

g4pD_taskb.txt vs g0pB_taskc.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

The vector space model has the following limitations:

g4pD_taskb.txt vs g0pC_taskd.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g4pD_taskb.txt vs g0pC_taske.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g4pD_taskb.txt vs g0pD_taskc.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g4pD_taskb.txt vs g0pC_taskb.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g4pD_taskb.txt vs g2pE_taske.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g4pD_taskb.txt vs g0pC_taska.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g4pD_taskb.txt vs g0pD_taska.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g4pD_taskb.txt vs g4pC_taska.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g4pD_taskb.txt vs g1pB_taskc.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

g4pD_taskb.txt vs g1pD_taskc.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g4pD_taskb.txt vs g2pB_taske.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

g4pD_taskb.txt vs g2pE_taskc.txt

PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. . It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. PageRank can be calculated for collections of documents of any size The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0. 5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.
Simplified algorithm
How PageRank Works
Assume a small universe of four web pages: A, B, C and D. The initial approximation of PageRank would be evenly divided between these four documents. Hence, each document would begin with an estimated PageRank of 0.25.
In the original form of PageRank initial values were simply 1. This meant that the sum of all pages was the total number of pages on the web. Later versions of PageRank (see the below formulas) would assume a probability distribution between 0 and 1. Here we're going to simply use a probability distribution hence the initial value of 0.25.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g0pA_taska.txt vs g0pB_taskb.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

g0pA_taska.txt vs g1pA_taskd.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

g0pA_taska.txt vs g2pA_taske.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

g0pA_taska.txt vs g4pE_taska.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

g0pA_taska.txt vs g0pA_taskd.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

g0pA_taska.txt vs g0pC_taskc.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

g0pA_taska.txt vs g1pB_taskd.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

g0pA_taska.txt vs g4pB_taskc.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

g0pA_taska.txt vs g2pC_taskb.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

g0pA_taska.txt vs g3pB_taskb.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

g0pA_taska.txt vs g3pB_taske.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

g0pA_taska.txt vs g3pC_taskb.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

g0pA_taska.txt vs g0pE_taske.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

g0pA_taska.txt vs g1pB_taska.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

g0pA_taska.txt vs g1pD_taskd.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

g0pA_taska.txt vs g2pA_taskd.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

g0pA_taska.txt vs g3pC_taske.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

g0pA_taska.txt vs g4pB_taskb.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

g0pA_taska.txt vs g4pE_taske.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

g0pA_taska.txt vs g1pD_taskb.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

g0pA_taska.txt vs g3pC_taska.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

g0pA_taska.txt vs g4pD_taskc.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

g0pA_taska.txt vs g4pE_taskb.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

g0pA_taska.txt vs g0pB_taskd.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g0pA_taska.txt vs g1pA_taska.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g0pA_taska.txt vs g1pA_taske.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g0pA_taska.txt vs g4pB_taske.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g0pA_taska.txt vs g2pE_taskd.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g0pA_taska.txt vs g4pB_taska.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g0pA_taska.txt vs g4pB_taskd.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g0pA_taska.txt vs g4pC_taskc.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g0pA_taska.txt vs g0pE_taskb.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g0pA_taska.txt vs g1pD_taske.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g0pA_taska.txt vs g2pB_taskb.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g0pA_taska.txt vs g2pB_taskd.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

g0pA_taska.txt vs g3pA_taske.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g0pA_taska.txt vs g4pC_taskd.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

g0pA_taska.txt vs orig_taskb.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

g0pA_taska.txt vs g0pE_taskc.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g0pA_taska.txt vs g2pB_taskc.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g0pA_taska.txt vs g2pC_taske.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g0pA_taska.txt vs g3pA_taskd.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g0pA_taska.txt vs g1pA_taskc.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g0pA_taska.txt vs g3pA_taskb.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g0pA_taska.txt vs orig_taska.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g0pA_taska.txt vs orig_taskd.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g0pA_taska.txt vs g0pA_taskb.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g0pA_taska.txt vs g0pB_taske.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g0pA_taska.txt vs g0pD_taskb.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g0pA_taska.txt vs g0pD_taske.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g0pA_taska.txt vs g3pB_taskc.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g0pA_taska.txt vs g3pC_taskc.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g0pA_taska.txt vs g4pC_taskb.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g0pA_taska.txt vs g4pC_taske.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

g0pA_taska.txt vs g0pA_taske.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g0pA_taska.txt vs g0pE_taska.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

g0pA_taska.txt vs g3pA_taska.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g0pA_taska.txt vs g3pB_taska.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g0pA_taska.txt vs g4pD_taska.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g0pA_taska.txt vs orig_taskc.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

g0pA_taska.txt vs g0pA_taskc.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g0pA_taska.txt vs g2pA_taska.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g0pA_taska.txt vs g2pC_taskd.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g0pA_taska.txt vs g4pD_taske.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g0pA_taska.txt vs g4pD_taskd.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g0pA_taska.txt vs g0pB_taska.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g0pA_taska.txt vs g1pB_taske.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g0pA_taska.txt vs g2pA_taskb.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

g0pA_taska.txt vs g2pA_taskc.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

g0pA_taska.txt vs g1pD_taska.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g0pA_taska.txt vs g2pB_taska.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g0pA_taska.txt vs g2pE_taskb.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g0pA_taska.txt vs g4pE_taskc.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g0pA_taska.txt vs g0pD_taskd.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g0pA_taska.txt vs g0pE_taskd.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g0pA_taska.txt vs g1pA_taskb.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g0pA_taska.txt vs g1pB_taskb.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g0pA_taska.txt vs g4pE_taskd.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g0pA_taska.txt vs g2pC_taska.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g0pA_taska.txt vs g2pC_taskc.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g0pA_taska.txt vs g2pE_taska.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

g0pA_taska.txt vs orig_taske.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

g0pA_taska.txt vs g0pB_taskc.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

The vector space model has the following limitations:

g0pA_taska.txt vs g0pC_taskd.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g0pA_taska.txt vs g0pC_taske.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g0pA_taska.txt vs g0pD_taskc.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g0pA_taska.txt vs g0pC_taskb.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g0pA_taska.txt vs g2pE_taske.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g0pA_taska.txt vs g0pC_taska.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g0pA_taska.txt vs g0pD_taska.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g0pA_taska.txt vs g4pC_taska.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g0pA_taska.txt vs g1pB_taskc.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

g0pA_taska.txt vs g1pD_taskc.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g0pA_taska.txt vs g2pB_taske.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

g0pA_taska.txt vs g2pE_taskc.txt

Inheritance is a basic concept of Object-Oriented Programming where
the basic idea is to create new classes that add extra detail to
existing classes. This is done by allowing the new classes to reuse
the methods and variables of the existing classes and new methods and
classes are added to specialise the new class. Inheritance models the
“is-kind-of” relationship between entities (or objects), for example,
postgraduates and undergraduates are both kinds of student. This kind
of relationship can be visualised as a tree structure, where ‘student’
would be the more general root node and both ‘postgraduate’ and
‘undergraduate’ would be more specialised extensions of the ‘student’
node (or the child nodes). In this relationship ‘student’ would be
known as the superclass or parent class whereas, ‘postgraduate’ would
be known as the subclass or child class because the ‘postgraduate’
class extends the ‘student’ class.

Inheritance can occur on several layers, where if visualised would
display a larger tree structure. For example, we could further extend
the ‘postgraduate’ node by adding two extra extended classes to it
called, ‘MSc Student’ and ‘PhD Student’ as both these types of student
are kinds of postgraduate student. This would mean that both the ‘MSc
Student’ and ‘PhD Student’ classes would inherit methods and variables
from both the ‘postgraduate’ and ‘student classes’.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g0pB_taskb.txt vs g1pA_taskd.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

g0pB_taskb.txt vs g2pA_taske.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

g0pB_taskb.txt vs g4pE_taska.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

g0pB_taskb.txt vs g0pA_taskd.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

g0pB_taskb.txt vs g0pC_taskc.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

g0pB_taskb.txt vs g1pB_taskd.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

g0pB_taskb.txt vs g4pB_taskc.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

g0pB_taskb.txt vs g2pC_taskb.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

g0pB_taskb.txt vs g3pB_taskb.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

g0pB_taskb.txt vs g3pB_taske.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

g0pB_taskb.txt vs g3pC_taskb.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

g0pB_taskb.txt vs g0pE_taske.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

g0pB_taskb.txt vs g1pB_taska.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

g0pB_taskb.txt vs g1pD_taskd.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

g0pB_taskb.txt vs g2pA_taskd.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

g0pB_taskb.txt vs g3pC_taske.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

g0pB_taskb.txt vs g4pB_taskb.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

g0pB_taskb.txt vs g4pE_taske.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

g0pB_taskb.txt vs g1pD_taskb.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

g0pB_taskb.txt vs g3pC_taska.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

g0pB_taskb.txt vs g4pD_taskc.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

g0pB_taskb.txt vs g4pE_taskb.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

g0pB_taskb.txt vs g0pB_taskd.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g0pB_taskb.txt vs g1pA_taska.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g0pB_taskb.txt vs g1pA_taske.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g0pB_taskb.txt vs g4pB_taske.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g0pB_taskb.txt vs g2pE_taskd.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g0pB_taskb.txt vs g4pB_taska.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g0pB_taskb.txt vs g4pB_taskd.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g0pB_taskb.txt vs g4pC_taskc.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g0pB_taskb.txt vs g0pE_taskb.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g0pB_taskb.txt vs g1pD_taske.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g0pB_taskb.txt vs g2pB_taskb.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g0pB_taskb.txt vs g2pB_taskd.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

g0pB_taskb.txt vs g3pA_taske.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g0pB_taskb.txt vs g4pC_taskd.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

g0pB_taskb.txt vs orig_taskb.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

g0pB_taskb.txt vs g0pE_taskc.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g0pB_taskb.txt vs g2pB_taskc.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g0pB_taskb.txt vs g2pC_taske.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g0pB_taskb.txt vs g3pA_taskd.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g0pB_taskb.txt vs g1pA_taskc.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g0pB_taskb.txt vs g3pA_taskb.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g0pB_taskb.txt vs orig_taska.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g0pB_taskb.txt vs orig_taskd.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g0pB_taskb.txt vs g0pA_taskb.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g0pB_taskb.txt vs g0pB_taske.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g0pB_taskb.txt vs g0pD_taskb.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g0pB_taskb.txt vs g0pD_taske.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g0pB_taskb.txt vs g3pB_taskc.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g0pB_taskb.txt vs g3pC_taskc.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g0pB_taskb.txt vs g4pC_taskb.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g0pB_taskb.txt vs g4pC_taske.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

g0pB_taskb.txt vs g0pA_taske.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g0pB_taskb.txt vs g0pE_taska.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

g0pB_taskb.txt vs g3pA_taska.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g0pB_taskb.txt vs g3pB_taska.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g0pB_taskb.txt vs g4pD_taska.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g0pB_taskb.txt vs orig_taskc.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

g0pB_taskb.txt vs g0pA_taskc.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g0pB_taskb.txt vs g2pA_taska.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g0pB_taskb.txt vs g2pC_taskd.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g0pB_taskb.txt vs g4pD_taske.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g0pB_taskb.txt vs g4pD_taskd.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g0pB_taskb.txt vs g0pB_taska.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g0pB_taskb.txt vs g1pB_taske.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g0pB_taskb.txt vs g2pA_taskb.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

g0pB_taskb.txt vs g2pA_taskc.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

g0pB_taskb.txt vs g1pD_taska.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g0pB_taskb.txt vs g2pB_taska.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g0pB_taskb.txt vs g2pE_taskb.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g0pB_taskb.txt vs g4pE_taskc.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g0pB_taskb.txt vs g0pD_taskd.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g0pB_taskb.txt vs g0pE_taskd.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g0pB_taskb.txt vs g1pA_taskb.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g0pB_taskb.txt vs g1pB_taskb.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g0pB_taskb.txt vs g4pE_taskd.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g0pB_taskb.txt vs g2pC_taska.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g0pB_taskb.txt vs g2pC_taskc.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g0pB_taskb.txt vs g2pE_taska.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

g0pB_taskb.txt vs orig_taske.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

g0pB_taskb.txt vs g0pB_taskc.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

The vector space model has the following limitations:

g0pB_taskb.txt vs g0pC_taskd.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g0pB_taskb.txt vs g0pC_taske.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g0pB_taskb.txt vs g0pD_taskc.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g0pB_taskb.txt vs g0pC_taskb.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g0pB_taskb.txt vs g2pE_taske.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g0pB_taskb.txt vs g0pC_taska.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g0pB_taskb.txt vs g0pD_taska.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g0pB_taskb.txt vs g4pC_taska.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g0pB_taskb.txt vs g1pB_taskc.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

g0pB_taskb.txt vs g1pD_taskc.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g0pB_taskb.txt vs g2pB_taske.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

g0pB_taskb.txt vs g2pE_taskc.txt

PageRank (PR) refers to both the concept and the Google system used
for ranking the importance of pages on the web. The “PageRank” of a
site refers to its importance or value on the web in relation to the
rest of the sites that have been “PageRank”ed.

The algorithm basically works like a popularity contest – if your site
is linked to by popular websites, then your site is considered more
popular. However, the PR doesn't just apply to the website as a whole
– different pages within a website get given different PRs dependent
on a number of factors:

* Inbound links (backlinks) – how many pages (other than the ones on your website) link to this particular page

* Outbound links (forward links) – how many external pages the particular page links to

* Dangling links – how many pages with no external links are linked to from a particular page

* Deep links – how many links that are not the home page are linked to from a particular page

PR tries to emulate a “random surfer”. The algorithm includes a
dampening factor, which is the probability that a random surfer will
get bored and go and visit a new page - by default, this is 0.85. A
variation on this is the “intentional surfer”, where the importance of
a page is based on the actual visits to sites by users. This method is
used in the Google Toolbar, which reports back actual site visits to
Google.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g1pA_taskd.txt vs g2pA_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

g1pA_taskd.txt vs g4pE_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

g1pA_taskd.txt vs g0pA_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

g1pA_taskd.txt vs g0pC_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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g1pA_taskd.txt vs g1pB_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

g1pA_taskd.txt vs g4pB_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

g1pA_taskd.txt vs g2pC_taskb.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

g1pA_taskd.txt vs g3pB_taskb.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

g1pA_taskd.txt vs g3pB_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

g1pA_taskd.txt vs g3pC_taskb.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

g1pA_taskd.txt vs g0pE_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

g1pA_taskd.txt vs g1pB_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

g1pA_taskd.txt vs g1pD_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

g1pA_taskd.txt vs g2pA_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

g1pA_taskd.txt vs g3pC_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

g1pA_taskd.txt vs g4pB_taskb.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

g1pA_taskd.txt vs g4pE_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

g1pA_taskd.txt vs g1pD_taskb.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

g1pA_taskd.txt vs g3pC_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

g1pA_taskd.txt vs g4pD_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

g1pA_taskd.txt vs g4pE_taskb.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
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g1pA_taskd.txt vs g0pB_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g1pA_taskd.txt vs g1pA_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g1pA_taskd.txt vs g1pA_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g1pA_taskd.txt vs g4pB_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g1pA_taskd.txt vs g2pE_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g1pA_taskd.txt vs g4pB_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g1pA_taskd.txt vs g4pB_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g1pA_taskd.txt vs g4pC_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g1pA_taskd.txt vs g0pE_taskb.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g1pA_taskd.txt vs g1pD_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g1pA_taskd.txt vs g2pB_taskb.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g1pA_taskd.txt vs g2pB_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

g1pA_taskd.txt vs g3pA_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g1pA_taskd.txt vs g4pC_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

g1pA_taskd.txt vs orig_taskb.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

g1pA_taskd.txt vs g0pE_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g1pA_taskd.txt vs g2pB_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g1pA_taskd.txt vs g2pC_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g1pA_taskd.txt vs g3pA_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g1pA_taskd.txt vs g1pA_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g1pA_taskd.txt vs g3pA_taskb.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g1pA_taskd.txt vs orig_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g1pA_taskd.txt vs orig_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g1pA_taskd.txt vs g0pA_taskb.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g1pA_taskd.txt vs g0pB_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g1pA_taskd.txt vs g0pD_taskb.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g1pA_taskd.txt vs g0pD_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g1pA_taskd.txt vs g3pB_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g1pA_taskd.txt vs g3pC_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g1pA_taskd.txt vs g4pC_taskb.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g1pA_taskd.txt vs g4pC_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

g1pA_taskd.txt vs g0pA_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g1pA_taskd.txt vs g0pE_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

g1pA_taskd.txt vs g3pA_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g1pA_taskd.txt vs g3pB_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g1pA_taskd.txt vs g4pD_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g1pA_taskd.txt vs orig_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

g1pA_taskd.txt vs g0pA_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g1pA_taskd.txt vs g2pA_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g1pA_taskd.txt vs g2pC_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g1pA_taskd.txt vs g4pD_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g1pA_taskd.txt vs g4pD_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g1pA_taskd.txt vs g0pB_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g1pA_taskd.txt vs g1pB_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g1pA_taskd.txt vs g2pA_taskb.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

g1pA_taskd.txt vs g2pA_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

g1pA_taskd.txt vs g1pD_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g1pA_taskd.txt vs g2pB_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g1pA_taskd.txt vs g2pE_taskb.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g1pA_taskd.txt vs g4pE_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g1pA_taskd.txt vs g0pD_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g1pA_taskd.txt vs g0pE_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g1pA_taskd.txt vs g1pA_taskb.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g1pA_taskd.txt vs g1pB_taskb.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g1pA_taskd.txt vs g4pE_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g1pA_taskd.txt vs g2pC_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g1pA_taskd.txt vs g2pC_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g1pA_taskd.txt vs g2pE_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

g1pA_taskd.txt vs orig_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

g1pA_taskd.txt vs g0pB_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

The vector space model has the following limitations:

g1pA_taskd.txt vs g0pC_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g1pA_taskd.txt vs g0pC_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g1pA_taskd.txt vs g0pD_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g1pA_taskd.txt vs g0pC_taskb.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g1pA_taskd.txt vs g2pE_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g1pA_taskd.txt vs g0pC_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g1pA_taskd.txt vs g0pD_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g1pA_taskd.txt vs g4pC_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g1pA_taskd.txt vs g1pB_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

g1pA_taskd.txt vs g1pD_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g1pA_taskd.txt vs g2pB_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

g1pA_taskd.txt vs g2pE_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of two random events and is named after the Reverend Thomas Bayes (1702–1761), who studied how to compute a distribution for the parameter of a binomial distribution. It is valid in all common interpretations of probability. It plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. Applications of Bayes' theorem often assume the philosophy underlying Bayesian probability that uncertainty and degrees of belief can be measured as probabilities. One of Bayes' results (Proposition 5) gives a simple description of conditional probability, and shows that it can be expressed independently of the order in which things occur:
If there be two subsequent events, the probability of the second b/N and the probability of both together P/N, and it being first discovered that the second event has also happened, from hence I guess that the first event has also happened, the probability I am right [i.e., the conditional probability of the first event being true given that the second has also happened] is P/b. 
Note that the expression says nothing about the order in which the events occurred; it measures correlation, not causation.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g2pA_taske.txt vs g4pE_taska.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

g2pA_taske.txt vs g0pA_taskd.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

g2pA_taske.txt vs g0pC_taskc.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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g2pA_taske.txt vs g1pB_taskd.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

g2pA_taske.txt vs g4pB_taskc.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

g2pA_taske.txt vs g2pC_taskb.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

g2pA_taske.txt vs g3pB_taskb.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

g2pA_taske.txt vs g3pB_taske.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

g2pA_taske.txt vs g3pC_taskb.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

g2pA_taske.txt vs g0pE_taske.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

g2pA_taske.txt vs g1pB_taska.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

g2pA_taske.txt vs g1pD_taskd.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

g2pA_taske.txt vs g2pA_taskd.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

g2pA_taske.txt vs g3pC_taske.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

g2pA_taske.txt vs g4pB_taskb.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

g2pA_taske.txt vs g4pE_taske.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

g2pA_taske.txt vs g1pD_taskb.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

g2pA_taske.txt vs g3pC_taska.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

g2pA_taske.txt vs g4pD_taskc.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

g2pA_taske.txt vs g4pE_taskb.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

g2pA_taske.txt vs g0pB_taskd.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g2pA_taske.txt vs g1pA_taska.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g2pA_taske.txt vs g1pA_taske.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g2pA_taske.txt vs g4pB_taske.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g2pA_taske.txt vs g2pE_taskd.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g2pA_taske.txt vs g4pB_taska.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g2pA_taske.txt vs g4pB_taskd.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g2pA_taske.txt vs g4pC_taskc.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g2pA_taske.txt vs g0pE_taskb.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g2pA_taske.txt vs g1pD_taske.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g2pA_taske.txt vs g2pB_taskb.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g2pA_taske.txt vs g2pB_taskd.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

g2pA_taske.txt vs g3pA_taske.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g2pA_taske.txt vs g4pC_taskd.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

g2pA_taske.txt vs orig_taskb.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

g2pA_taske.txt vs g0pE_taskc.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g2pA_taske.txt vs g2pB_taskc.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g2pA_taske.txt vs g2pC_taske.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g2pA_taske.txt vs g3pA_taskd.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g2pA_taske.txt vs g1pA_taskc.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g2pA_taske.txt vs g3pA_taskb.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g2pA_taske.txt vs orig_taska.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g2pA_taske.txt vs orig_taskd.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g2pA_taske.txt vs g0pA_taskb.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g2pA_taske.txt vs g0pB_taske.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g2pA_taske.txt vs g0pD_taskb.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g2pA_taske.txt vs g0pD_taske.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g2pA_taske.txt vs g3pB_taskc.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g2pA_taske.txt vs g3pC_taskc.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g2pA_taske.txt vs g4pC_taskb.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g2pA_taske.txt vs g4pC_taske.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

g2pA_taske.txt vs g0pA_taske.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g2pA_taske.txt vs g0pE_taska.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

g2pA_taske.txt vs g3pA_taska.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g2pA_taske.txt vs g3pB_taska.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g2pA_taske.txt vs g4pD_taska.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g2pA_taske.txt vs orig_taskc.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

g2pA_taske.txt vs g0pA_taskc.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g2pA_taske.txt vs g2pA_taska.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g2pA_taske.txt vs g2pC_taskd.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g2pA_taske.txt vs g4pD_taske.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g2pA_taske.txt vs g4pD_taskd.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g2pA_taske.txt vs g0pB_taska.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g2pA_taske.txt vs g1pB_taske.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g2pA_taske.txt vs g2pA_taskb.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

g2pA_taske.txt vs g2pA_taskc.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

g2pA_taske.txt vs g1pD_taska.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g2pA_taske.txt vs g2pB_taska.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g2pA_taske.txt vs g2pE_taskb.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g2pA_taske.txt vs g4pE_taskc.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g2pA_taske.txt vs g0pD_taskd.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g2pA_taske.txt vs g0pE_taskd.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g2pA_taske.txt vs g1pA_taskb.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g2pA_taske.txt vs g1pB_taskb.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g2pA_taske.txt vs g4pE_taskd.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g2pA_taske.txt vs g2pC_taska.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g2pA_taske.txt vs g2pC_taskc.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g2pA_taske.txt vs g2pE_taska.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

g2pA_taske.txt vs orig_taske.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

g2pA_taske.txt vs g0pB_taskc.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

The vector space model has the following limitations:

g2pA_taske.txt vs g0pC_taskd.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g2pA_taske.txt vs g0pC_taske.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g2pA_taske.txt vs g0pD_taskc.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g2pA_taske.txt vs g0pC_taskb.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g2pA_taske.txt vs g2pE_taske.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g2pA_taske.txt vs g0pC_taska.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g2pA_taske.txt vs g0pD_taska.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g2pA_taske.txt vs g4pC_taska.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g2pA_taske.txt vs g1pB_taskc.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

g2pA_taske.txt vs g1pD_taskc.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g2pA_taske.txt vs g2pB_taske.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

g2pA_taske.txt vs g2pE_taskc.txt

Dynamic Programming is a very powerful mathematical technique, often utilised in programming, for solving optimization problems. Normally, minimizing or maximizing.
Greedy algorithms focus on making the best local choice at each decision making stage. Without a proof of correctness, such an algorithm is likely to fail. With Dynamic Programming, we can design our own algorithm which searches for all possibilities (which ensures correctness) whilst storing the results to avoid having to recomputed (leading to computational efficiency).
Dynamic Programming solves problems by combining the solutions of subproblems. These subproblems are not, however, independent. Subproblems can share subsubproblems, but the solution to one subproblem doesnt necessarily affect the solutions to other subproblems stemming from the same problem.
Dynamic Programming reduces computation time by solving subproblems in a bottom-up way. It stores the solution to a subproblem the first time it is solved, meaning that it can look up the solution when that subproblem is encountered subsequently. 
The key to Dynamic Programming is to find the structure of optimal solutions. The steps required are as follows:
1.	Generalise the structure of an optimal solution
2.	Recursively define the value of an optimal solution
3.	Compute the optimal solution values either top-down (with caching), or bottom-up using a table
4.	Generate the optimal solution of these computed values

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g4pE_taska.txt vs g0pA_taskd.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

g4pE_taska.txt vs g0pC_taskc.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

g4pE_taska.txt vs g1pB_taskd.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

g4pE_taska.txt vs g4pB_taskc.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

g4pE_taska.txt vs g2pC_taskb.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

g4pE_taska.txt vs g3pB_taskb.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

g4pE_taska.txt vs g3pB_taske.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

g4pE_taska.txt vs g3pC_taskb.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

g4pE_taska.txt vs g0pE_taske.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

g4pE_taska.txt vs g1pB_taska.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

g4pE_taska.txt vs g1pD_taskd.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

g4pE_taska.txt vs g2pA_taskd.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

g4pE_taska.txt vs g3pC_taske.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

g4pE_taska.txt vs g4pB_taskb.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

g4pE_taska.txt vs g4pE_taske.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

g4pE_taska.txt vs g1pD_taskb.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

g4pE_taska.txt vs g3pC_taska.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

g4pE_taska.txt vs g4pD_taskc.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

g4pE_taska.txt vs g4pE_taskb.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

g4pE_taska.txt vs g0pB_taskd.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g4pE_taska.txt vs g1pA_taska.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g4pE_taska.txt vs g1pA_taske.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g4pE_taska.txt vs g4pB_taske.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g4pE_taska.txt vs g2pE_taskd.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g4pE_taska.txt vs g4pB_taska.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g4pE_taska.txt vs g4pB_taskd.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g4pE_taska.txt vs g4pC_taskc.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g4pE_taska.txt vs g0pE_taskb.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g4pE_taska.txt vs g1pD_taske.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g4pE_taska.txt vs g2pB_taskb.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g4pE_taska.txt vs g2pB_taskd.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

g4pE_taska.txt vs g3pA_taske.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g4pE_taska.txt vs g4pC_taskd.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

g4pE_taska.txt vs orig_taskb.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

g4pE_taska.txt vs g0pE_taskc.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g4pE_taska.txt vs g2pB_taskc.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g4pE_taska.txt vs g2pC_taske.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g4pE_taska.txt vs g3pA_taskd.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g4pE_taska.txt vs g1pA_taskc.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g4pE_taska.txt vs g3pA_taskb.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g4pE_taska.txt vs orig_taska.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g4pE_taska.txt vs orig_taskd.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g4pE_taska.txt vs g0pA_taskb.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g4pE_taska.txt vs g0pB_taske.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g4pE_taska.txt vs g0pD_taskb.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g4pE_taska.txt vs g0pD_taske.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g4pE_taska.txt vs g3pB_taskc.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g4pE_taska.txt vs g3pC_taskc.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g4pE_taska.txt vs g4pC_taskb.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g4pE_taska.txt vs g4pC_taske.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

g4pE_taska.txt vs g0pA_taske.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g4pE_taska.txt vs g0pE_taska.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

g4pE_taska.txt vs g3pA_taska.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g4pE_taska.txt vs g3pB_taska.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g4pE_taska.txt vs g4pD_taska.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g4pE_taska.txt vs orig_taskc.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

g4pE_taska.txt vs g0pA_taskc.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g4pE_taska.txt vs g2pA_taska.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g4pE_taska.txt vs g2pC_taskd.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g4pE_taska.txt vs g4pD_taske.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g4pE_taska.txt vs g4pD_taskd.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g4pE_taska.txt vs g0pB_taska.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g4pE_taska.txt vs g1pB_taske.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g4pE_taska.txt vs g2pA_taskb.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

g4pE_taska.txt vs g2pA_taskc.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

g4pE_taska.txt vs g1pD_taska.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g4pE_taska.txt vs g2pB_taska.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g4pE_taska.txt vs g2pE_taskb.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g4pE_taska.txt vs g4pE_taskc.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g4pE_taska.txt vs g0pD_taskd.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g4pE_taska.txt vs g0pE_taskd.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g4pE_taska.txt vs g1pA_taskb.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g4pE_taska.txt vs g1pB_taskb.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g4pE_taska.txt vs g4pE_taskd.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g4pE_taska.txt vs g2pC_taska.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g4pE_taska.txt vs g2pC_taskc.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g4pE_taska.txt vs g2pE_taska.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

g4pE_taska.txt vs orig_taske.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

g4pE_taska.txt vs g0pB_taskc.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

The vector space model has the following limitations:

g4pE_taska.txt vs g0pC_taskd.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g4pE_taska.txt vs g0pC_taske.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g4pE_taska.txt vs g0pD_taskc.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g4pE_taska.txt vs g0pC_taskb.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g4pE_taska.txt vs g2pE_taske.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g4pE_taska.txt vs g0pC_taska.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g4pE_taska.txt vs g0pD_taska.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g4pE_taska.txt vs g4pC_taska.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g4pE_taska.txt vs g1pB_taskc.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

g4pE_taska.txt vs g1pD_taskc.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g4pE_taska.txt vs g2pB_taske.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

g4pE_taska.txt vs g2pE_taskc.txt

Object oriented programming is a  style of programming that supports encapsulation, inheritance, and polymorphism. Inheritance means derived  a new class from the base class.  We can also say there are parents class and child classes in inheritance.  Inheritance was firstly derived in 1967.
The child class has all the features of parents class or we can say the base class more over it may also include some additional features.  Inheritance is used for modification and implementation new features in computer programming language.It is possible that child class has all the attributes of parents class but it is not possible that all the attributes of child class must have in base class or parent class.
I categorization in computer language also inheritance is a useful tool.categorization define as a powerful  feature.it  has been also used in generalisation and in human learning. In some areas less information need to be stored.
Generlisation also some time known as inheritance. The main reason behind this is a hierarchi structure of objects and classes. We can understand  this mechanism by some examples: like fruit is aq main class and mangoes apple ,orange is child classs of the main class.So obviously inherit all the properties of fruit class.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g0pA_taskd.txt vs g0pC_taskc.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

g0pA_taskd.txt vs g1pB_taskd.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

g0pA_taskd.txt vs g4pB_taskc.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

g0pA_taskd.txt vs g2pC_taskb.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

g0pA_taskd.txt vs g3pB_taskb.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

g0pA_taskd.txt vs g3pB_taske.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

g0pA_taskd.txt vs g3pC_taskb.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

g0pA_taskd.txt vs g0pE_taske.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

g0pA_taskd.txt vs g1pB_taska.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

g0pA_taskd.txt vs g1pD_taskd.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

g0pA_taskd.txt vs g2pA_taskd.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

g0pA_taskd.txt vs g3pC_taske.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

g0pA_taskd.txt vs g4pB_taskb.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

g0pA_taskd.txt vs g4pE_taske.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

g0pA_taskd.txt vs g1pD_taskb.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

g0pA_taskd.txt vs g3pC_taska.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

g0pA_taskd.txt vs g4pD_taskc.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

g0pA_taskd.txt vs g4pE_taskb.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

g0pA_taskd.txt vs g0pB_taskd.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g0pA_taskd.txt vs g1pA_taska.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g0pA_taskd.txt vs g1pA_taske.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g0pA_taskd.txt vs g4pB_taske.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g0pA_taskd.txt vs g2pE_taskd.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g0pA_taskd.txt vs g4pB_taska.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g0pA_taskd.txt vs g4pB_taskd.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g0pA_taskd.txt vs g4pC_taskc.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g0pA_taskd.txt vs g0pE_taskb.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g0pA_taskd.txt vs g1pD_taske.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g0pA_taskd.txt vs g2pB_taskb.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g0pA_taskd.txt vs g2pB_taskd.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

g0pA_taskd.txt vs g3pA_taske.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g0pA_taskd.txt vs g4pC_taskd.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

g0pA_taskd.txt vs orig_taskb.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

g0pA_taskd.txt vs g0pE_taskc.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g0pA_taskd.txt vs g2pB_taskc.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g0pA_taskd.txt vs g2pC_taske.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g0pA_taskd.txt vs g3pA_taskd.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g0pA_taskd.txt vs g1pA_taskc.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g0pA_taskd.txt vs g3pA_taskb.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g0pA_taskd.txt vs orig_taska.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g0pA_taskd.txt vs orig_taskd.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g0pA_taskd.txt vs g0pA_taskb.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g0pA_taskd.txt vs g0pB_taske.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g0pA_taskd.txt vs g0pD_taskb.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g0pA_taskd.txt vs g0pD_taske.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g0pA_taskd.txt vs g3pB_taskc.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g0pA_taskd.txt vs g3pC_taskc.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g0pA_taskd.txt vs g4pC_taskb.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g0pA_taskd.txt vs g4pC_taske.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

g0pA_taskd.txt vs g0pA_taske.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g0pA_taskd.txt vs g0pE_taska.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

g0pA_taskd.txt vs g3pA_taska.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g0pA_taskd.txt vs g3pB_taska.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g0pA_taskd.txt vs g4pD_taska.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g0pA_taskd.txt vs orig_taskc.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

g0pA_taskd.txt vs g0pA_taskc.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g0pA_taskd.txt vs g2pA_taska.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g0pA_taskd.txt vs g2pC_taskd.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g0pA_taskd.txt vs g4pD_taske.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g0pA_taskd.txt vs g4pD_taskd.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g0pA_taskd.txt vs g0pB_taska.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g0pA_taskd.txt vs g1pB_taske.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g0pA_taskd.txt vs g2pA_taskb.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

g0pA_taskd.txt vs g2pA_taskc.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

g0pA_taskd.txt vs g1pD_taska.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g0pA_taskd.txt vs g2pB_taska.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g0pA_taskd.txt vs g2pE_taskb.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g0pA_taskd.txt vs g4pE_taskc.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g0pA_taskd.txt vs g0pD_taskd.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g0pA_taskd.txt vs g0pE_taskd.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g0pA_taskd.txt vs g1pA_taskb.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g0pA_taskd.txt vs g1pB_taskb.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g0pA_taskd.txt vs g4pE_taskd.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g0pA_taskd.txt vs g2pC_taska.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g0pA_taskd.txt vs g2pC_taskc.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g0pA_taskd.txt vs g2pE_taska.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

g0pA_taskd.txt vs orig_taske.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

g0pA_taskd.txt vs g0pB_taskc.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

The vector space model has the following limitations:

g0pA_taskd.txt vs g0pC_taskd.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g0pA_taskd.txt vs g0pC_taske.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g0pA_taskd.txt vs g0pD_taskc.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g0pA_taskd.txt vs g0pC_taskb.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g0pA_taskd.txt vs g2pE_taske.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g0pA_taskd.txt vs g0pC_taska.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g0pA_taskd.txt vs g0pD_taska.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g0pA_taskd.txt vs g4pC_taska.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g0pA_taskd.txt vs g1pB_taskc.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

g0pA_taskd.txt vs g1pD_taskc.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g0pA_taskd.txt vs g2pB_taske.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

g0pA_taskd.txt vs g2pE_taskc.txt

Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g0pC_taskc.txt vs g1pB_taskd.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

g0pC_taskc.txt vs g4pB_taskc.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

g0pC_taskc.txt vs g2pC_taskb.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

g0pC_taskc.txt vs g3pB_taskb.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

g0pC_taskc.txt vs g3pB_taske.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

g0pC_taskc.txt vs g3pC_taskb.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

g0pC_taskc.txt vs g0pE_taske.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

g0pC_taskc.txt vs g1pB_taska.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

g0pC_taskc.txt vs g1pD_taskd.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

g0pC_taskc.txt vs g2pA_taskd.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

g0pC_taskc.txt vs g3pC_taske.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

g0pC_taskc.txt vs g4pB_taskb.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

g0pC_taskc.txt vs g4pE_taske.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

g0pC_taskc.txt vs g1pD_taskb.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

g0pC_taskc.txt vs g3pC_taska.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

g0pC_taskc.txt vs g4pD_taskc.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

g0pC_taskc.txt vs g4pE_taskb.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
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g0pC_taskc.txt vs g0pB_taskd.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g0pC_taskc.txt vs g1pA_taska.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g0pC_taskc.txt vs g1pA_taske.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g0pC_taskc.txt vs g4pB_taske.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g0pC_taskc.txt vs g2pE_taskd.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g0pC_taskc.txt vs g4pB_taska.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g0pC_taskc.txt vs g4pB_taskd.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g0pC_taskc.txt vs g4pC_taskc.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g0pC_taskc.txt vs g0pE_taskb.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g0pC_taskc.txt vs g1pD_taske.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g0pC_taskc.txt vs g2pB_taskb.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g0pC_taskc.txt vs g2pB_taskd.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

g0pC_taskc.txt vs g3pA_taske.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g0pC_taskc.txt vs g4pC_taskd.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

g0pC_taskc.txt vs orig_taskb.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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g0pC_taskc.txt vs g0pE_taskc.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g0pC_taskc.txt vs g2pB_taskc.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g0pC_taskc.txt vs g2pC_taske.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g0pC_taskc.txt vs g3pA_taskd.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g0pC_taskc.txt vs g1pA_taskc.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g0pC_taskc.txt vs g3pA_taskb.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g0pC_taskc.txt vs orig_taska.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g0pC_taskc.txt vs orig_taskd.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g0pC_taskc.txt vs g0pA_taskb.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g0pC_taskc.txt vs g0pB_taske.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g0pC_taskc.txt vs g0pD_taskb.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g0pC_taskc.txt vs g0pD_taske.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g0pC_taskc.txt vs g3pB_taskc.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g0pC_taskc.txt vs g3pC_taskc.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g0pC_taskc.txt vs g4pC_taskb.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g0pC_taskc.txt vs g4pC_taske.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

g0pC_taskc.txt vs g0pA_taske.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g0pC_taskc.txt vs g0pE_taska.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

g0pC_taskc.txt vs g3pA_taska.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g0pC_taskc.txt vs g3pB_taska.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g0pC_taskc.txt vs g4pD_taska.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g0pC_taskc.txt vs orig_taskc.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

g0pC_taskc.txt vs g0pA_taskc.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g0pC_taskc.txt vs g2pA_taska.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g0pC_taskc.txt vs g2pC_taskd.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g0pC_taskc.txt vs g4pD_taske.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g0pC_taskc.txt vs g4pD_taskd.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g0pC_taskc.txt vs g0pB_taska.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g0pC_taskc.txt vs g1pB_taske.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g0pC_taskc.txt vs g2pA_taskb.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

g0pC_taskc.txt vs g2pA_taskc.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

g0pC_taskc.txt vs g1pD_taska.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g0pC_taskc.txt vs g2pB_taska.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g0pC_taskc.txt vs g2pE_taskb.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g0pC_taskc.txt vs g4pE_taskc.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g0pC_taskc.txt vs g0pD_taskd.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g0pC_taskc.txt vs g0pE_taskd.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g0pC_taskc.txt vs g1pA_taskb.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g0pC_taskc.txt vs g1pB_taskb.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g0pC_taskc.txt vs g4pE_taskd.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g0pC_taskc.txt vs g2pC_taska.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g0pC_taskc.txt vs g2pC_taskc.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g0pC_taskc.txt vs g2pE_taska.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

g0pC_taskc.txt vs orig_taske.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

g0pC_taskc.txt vs g0pB_taskc.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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The vector space model has the following limitations:

g0pC_taskc.txt vs g0pC_taskd.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g0pC_taskc.txt vs g0pC_taske.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g0pC_taskc.txt vs g0pD_taskc.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g0pC_taskc.txt vs g0pC_taskb.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g0pC_taskc.txt vs g2pE_taske.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g0pC_taskc.txt vs g0pC_taska.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g0pC_taskc.txt vs g0pD_taska.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g0pC_taskc.txt vs g4pC_taska.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
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In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g0pC_taskc.txt vs g1pB_taskc.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

g0pC_taskc.txt vs g1pD_taskc.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g0pC_taskc.txt vs g2pB_taske.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

g0pC_taskc.txt vs g2pE_taskc.txt

The vector space model is where each document is viewed as a bag of words, where there order has little significance. Each document is a vector where each word is a dimension. The vector is then constucted of the frequency of eacher word (dimension). The draw back to this approach is that the length of the document as an inpact on the vector, to compensate for this you can comput the cosine similarity between your two comparism documents. This will find the difference between the two vectors (the dot product), ignoreing the size of them.

Inorder to query the search space, the query can also be represented as a vector, then you find the document whos vector has the greatest cosine similarities to your query. There are a number of wighting sceems which can be incoperated inorder to increase the accuracy of the vextors.

There are some drawbacks with this approach, Computing the cosine similarities between each vector can be expensive as the number of dimensions can be in the thousands, To tackle this problem you can use inverted indexs and then a series heuristics inorder to inprove on this.
to top

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g1pB_taskd.txt vs g4pB_taskc.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

g1pB_taskd.txt vs g2pC_taskb.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

g1pB_taskd.txt vs g3pB_taskb.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

g1pB_taskd.txt vs g3pB_taske.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

g1pB_taskd.txt vs g3pC_taskb.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

g1pB_taskd.txt vs g0pE_taske.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

g1pB_taskd.txt vs g1pB_taska.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

g1pB_taskd.txt vs g1pD_taskd.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

g1pB_taskd.txt vs g2pA_taskd.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

g1pB_taskd.txt vs g3pC_taske.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

g1pB_taskd.txt vs g4pB_taskb.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

g1pB_taskd.txt vs g4pE_taske.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

g1pB_taskd.txt vs g1pD_taskb.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

g1pB_taskd.txt vs g3pC_taska.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

g1pB_taskd.txt vs g4pD_taskc.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

g1pB_taskd.txt vs g4pE_taskb.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

g1pB_taskd.txt vs g0pB_taskd.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g1pB_taskd.txt vs g1pA_taska.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g1pB_taskd.txt vs g1pA_taske.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g1pB_taskd.txt vs g4pB_taske.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g1pB_taskd.txt vs g2pE_taskd.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g1pB_taskd.txt vs g4pB_taska.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g1pB_taskd.txt vs g4pB_taskd.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g1pB_taskd.txt vs g4pC_taskc.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g1pB_taskd.txt vs g0pE_taskb.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g1pB_taskd.txt vs g1pD_taske.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g1pB_taskd.txt vs g2pB_taskb.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g1pB_taskd.txt vs g2pB_taskd.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

g1pB_taskd.txt vs g3pA_taske.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g1pB_taskd.txt vs g4pC_taskd.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

g1pB_taskd.txt vs orig_taskb.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

g1pB_taskd.txt vs g0pE_taskc.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g1pB_taskd.txt vs g2pB_taskc.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g1pB_taskd.txt vs g2pC_taske.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g1pB_taskd.txt vs g3pA_taskd.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g1pB_taskd.txt vs g1pA_taskc.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g1pB_taskd.txt vs g3pA_taskb.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g1pB_taskd.txt vs orig_taska.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g1pB_taskd.txt vs orig_taskd.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g1pB_taskd.txt vs g0pA_taskb.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g1pB_taskd.txt vs g0pB_taske.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g1pB_taskd.txt vs g0pD_taskb.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g1pB_taskd.txt vs g0pD_taske.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g1pB_taskd.txt vs g3pB_taskc.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g1pB_taskd.txt vs g3pC_taskc.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g1pB_taskd.txt vs g4pC_taskb.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g1pB_taskd.txt vs g4pC_taske.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

g1pB_taskd.txt vs g0pA_taske.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g1pB_taskd.txt vs g0pE_taska.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

g1pB_taskd.txt vs g3pA_taska.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g1pB_taskd.txt vs g3pB_taska.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g1pB_taskd.txt vs g4pD_taska.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g1pB_taskd.txt vs orig_taskc.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

g1pB_taskd.txt vs g0pA_taskc.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g1pB_taskd.txt vs g2pA_taska.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g1pB_taskd.txt vs g2pC_taskd.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g1pB_taskd.txt vs g4pD_taske.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g1pB_taskd.txt vs g4pD_taskd.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g1pB_taskd.txt vs g0pB_taska.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g1pB_taskd.txt vs g1pB_taske.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g1pB_taskd.txt vs g2pA_taskb.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

g1pB_taskd.txt vs g2pA_taskc.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

g1pB_taskd.txt vs g1pD_taska.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g1pB_taskd.txt vs g2pB_taska.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g1pB_taskd.txt vs g2pE_taskb.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g1pB_taskd.txt vs g4pE_taskc.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g1pB_taskd.txt vs g0pD_taskd.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g1pB_taskd.txt vs g0pE_taskd.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g1pB_taskd.txt vs g1pA_taskb.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g1pB_taskd.txt vs g1pB_taskb.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g1pB_taskd.txt vs g4pE_taskd.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g1pB_taskd.txt vs g2pC_taska.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g1pB_taskd.txt vs g2pC_taskc.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g1pB_taskd.txt vs g2pE_taska.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

g1pB_taskd.txt vs orig_taske.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

g1pB_taskd.txt vs g0pB_taskc.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

The vector space model has the following limitations:

g1pB_taskd.txt vs g0pC_taskd.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g1pB_taskd.txt vs g0pC_taske.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g1pB_taskd.txt vs g0pD_taskc.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g1pB_taskd.txt vs g0pC_taskb.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g1pB_taskd.txt vs g2pE_taske.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g1pB_taskd.txt vs g0pC_taska.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g1pB_taskd.txt vs g0pD_taska.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g1pB_taskd.txt vs g4pC_taska.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g1pB_taskd.txt vs g1pB_taskc.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

g1pB_taskd.txt vs g1pD_taskc.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g1pB_taskd.txt vs g2pB_taske.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

g1pB_taskd.txt vs g2pE_taskc.txt

Bayes� theorem relates the conditional and marginal probabilities of two random events.  It is mainly used to calculate the probability of one event�s outcome given that a previous event happened.  For example, the probability that a doctors diagnosis is correct given that the doctor had previously observed symptoms in the patient.  Bayes� theorem can be used for all forms of probability, however it is currently at the centre of a debate concerning the ways in which probabilities should be assigned in applications. 
The theorem states that the probability of Event A happening given Event B is the probability of B given A multiplied by the probability of A regardless of B all divided by the probability of B regardless of A which acts as a normalising constant.  Bayes� theorem formed in this way basically details how one�s beliefs about Event A are renewed or updated knowing that Event B happened.  When calculating conditional probabilities such as these, it is often useful to create a table containing the number of occurrences, or relative frequencies, of each outcome for each of the variables independently.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g4pB_taskc.txt vs g2pC_taskb.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

g4pB_taskc.txt vs g3pB_taskb.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

g4pB_taskc.txt vs g3pB_taske.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

g4pB_taskc.txt vs g3pC_taskb.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

g4pB_taskc.txt vs g0pE_taske.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

g4pB_taskc.txt vs g1pB_taska.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

g4pB_taskc.txt vs g1pD_taskd.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

g4pB_taskc.txt vs g2pA_taskd.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

g4pB_taskc.txt vs g3pC_taske.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

g4pB_taskc.txt vs g4pB_taskb.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

g4pB_taskc.txt vs g4pE_taske.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

g4pB_taskc.txt vs g1pD_taskb.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

g4pB_taskc.txt vs g3pC_taska.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

g4pB_taskc.txt vs g4pD_taskc.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

g4pB_taskc.txt vs g4pE_taskb.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

g4pB_taskc.txt vs g0pB_taskd.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g4pB_taskc.txt vs g1pA_taska.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g4pB_taskc.txt vs g1pA_taske.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g4pB_taskc.txt vs g4pB_taske.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g4pB_taskc.txt vs g2pE_taskd.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g4pB_taskc.txt vs g4pB_taska.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g4pB_taskc.txt vs g4pB_taskd.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g4pB_taskc.txt vs g4pC_taskc.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g4pB_taskc.txt vs g0pE_taskb.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g4pB_taskc.txt vs g1pD_taske.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g4pB_taskc.txt vs g2pB_taskb.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g4pB_taskc.txt vs g2pB_taskd.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

g4pB_taskc.txt vs g3pA_taske.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g4pB_taskc.txt vs g4pC_taskd.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

g4pB_taskc.txt vs orig_taskb.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

g4pB_taskc.txt vs g0pE_taskc.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g4pB_taskc.txt vs g2pB_taskc.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g4pB_taskc.txt vs g2pC_taske.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g4pB_taskc.txt vs g3pA_taskd.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g4pB_taskc.txt vs g1pA_taskc.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g4pB_taskc.txt vs g3pA_taskb.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g4pB_taskc.txt vs orig_taska.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g4pB_taskc.txt vs orig_taskd.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g4pB_taskc.txt vs g0pA_taskb.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g4pB_taskc.txt vs g0pB_taske.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g4pB_taskc.txt vs g0pD_taskb.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g4pB_taskc.txt vs g0pD_taske.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g4pB_taskc.txt vs g3pB_taskc.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g4pB_taskc.txt vs g3pC_taskc.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g4pB_taskc.txt vs g4pC_taskb.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g4pB_taskc.txt vs g4pC_taske.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

g4pB_taskc.txt vs g0pA_taske.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g4pB_taskc.txt vs g0pE_taska.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

g4pB_taskc.txt vs g3pA_taska.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g4pB_taskc.txt vs g3pB_taska.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g4pB_taskc.txt vs g4pD_taska.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g4pB_taskc.txt vs orig_taskc.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

g4pB_taskc.txt vs g0pA_taskc.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g4pB_taskc.txt vs g2pA_taska.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g4pB_taskc.txt vs g2pC_taskd.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g4pB_taskc.txt vs g4pD_taske.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g4pB_taskc.txt vs g4pD_taskd.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g4pB_taskc.txt vs g0pB_taska.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g4pB_taskc.txt vs g1pB_taske.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g4pB_taskc.txt vs g2pA_taskb.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

g4pB_taskc.txt vs g2pA_taskc.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

g4pB_taskc.txt vs g1pD_taska.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g4pB_taskc.txt vs g2pB_taska.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g4pB_taskc.txt vs g2pE_taskb.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g4pB_taskc.txt vs g4pE_taskc.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g4pB_taskc.txt vs g0pD_taskd.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g4pB_taskc.txt vs g0pE_taskd.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g4pB_taskc.txt vs g1pA_taskb.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g4pB_taskc.txt vs g1pB_taskb.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g4pB_taskc.txt vs g4pE_taskd.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g4pB_taskc.txt vs g2pC_taska.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g4pB_taskc.txt vs g2pC_taskc.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g4pB_taskc.txt vs g2pE_taska.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

g4pB_taskc.txt vs orig_taske.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

g4pB_taskc.txt vs g0pB_taskc.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

The vector space model has the following limitations:

g4pB_taskc.txt vs g0pC_taskd.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g4pB_taskc.txt vs g0pC_taske.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g4pB_taskc.txt vs g0pD_taskc.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g4pB_taskc.txt vs g0pC_taskb.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g4pB_taskc.txt vs g2pE_taske.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g4pB_taskc.txt vs g0pC_taska.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g4pB_taskc.txt vs g0pD_taska.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g4pB_taskc.txt vs g4pC_taska.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g4pB_taskc.txt vs g1pB_taskc.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

g4pB_taskc.txt vs g1pD_taskc.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g4pB_taskc.txt vs g2pB_taske.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

g4pB_taskc.txt vs g2pE_taskc.txt

The vector space model (or term vector model) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. It was used in the first time in the SMART Information Retrieval System.

A document is represented as a vector. Each and every dimension corresponds to a separate term. If a term exists in a document, its value in the vector is not equal to zero. A couple of different algorithms of computing these values, also known as (term) weights, have been created. One of the most popular schemes is tf-idf weighting.

The definition of term is dependent on the application. Typically terms are keywords, single words or longer phrases. Provided that words are selected to be the terms, the dimensionality of the vector is equal to the number of words in the vocabulary.


It is easiest to calculate the cosinus of the angle between the vectors instead of the angle by the formula:

    cos(theta)=v1.v2/(||v1||||v2||)

A null cosinus value says that the query and document vector were orthogonal and had no match which means that no term of the query was ever encountered in the document.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g2pC_taskb.txt vs g3pB_taskb.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

g2pC_taskb.txt vs g3pB_taske.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

g2pC_taskb.txt vs g3pC_taskb.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

g2pC_taskb.txt vs g0pE_taske.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

g2pC_taskb.txt vs g1pB_taska.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

g2pC_taskb.txt vs g1pD_taskd.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

g2pC_taskb.txt vs g2pA_taskd.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

g2pC_taskb.txt vs g3pC_taske.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

g2pC_taskb.txt vs g4pB_taskb.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

g2pC_taskb.txt vs g4pE_taske.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

g2pC_taskb.txt vs g1pD_taskb.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

g2pC_taskb.txt vs g3pC_taska.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

g2pC_taskb.txt vs g4pD_taskc.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

g2pC_taskb.txt vs g4pE_taskb.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

g2pC_taskb.txt vs g0pB_taskd.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g2pC_taskb.txt vs g1pA_taska.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g2pC_taskb.txt vs g1pA_taske.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g2pC_taskb.txt vs g4pB_taske.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g2pC_taskb.txt vs g2pE_taskd.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g2pC_taskb.txt vs g4pB_taska.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g2pC_taskb.txt vs g4pB_taskd.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g2pC_taskb.txt vs g4pC_taskc.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g2pC_taskb.txt vs g0pE_taskb.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g2pC_taskb.txt vs g1pD_taske.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g2pC_taskb.txt vs g2pB_taskb.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g2pC_taskb.txt vs g2pB_taskd.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

g2pC_taskb.txt vs g3pA_taske.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g2pC_taskb.txt vs g4pC_taskd.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

g2pC_taskb.txt vs orig_taskb.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

g2pC_taskb.txt vs g0pE_taskc.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g2pC_taskb.txt vs g2pB_taskc.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g2pC_taskb.txt vs g2pC_taske.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g2pC_taskb.txt vs g3pA_taskd.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g2pC_taskb.txt vs g1pA_taskc.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g2pC_taskb.txt vs g3pA_taskb.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g2pC_taskb.txt vs orig_taska.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g2pC_taskb.txt vs orig_taskd.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g2pC_taskb.txt vs g0pA_taskb.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g2pC_taskb.txt vs g0pB_taske.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g2pC_taskb.txt vs g0pD_taskb.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g2pC_taskb.txt vs g0pD_taske.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g2pC_taskb.txt vs g3pB_taskc.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g2pC_taskb.txt vs g3pC_taskc.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g2pC_taskb.txt vs g4pC_taskb.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g2pC_taskb.txt vs g4pC_taske.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

g2pC_taskb.txt vs g0pA_taske.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g2pC_taskb.txt vs g0pE_taska.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

g2pC_taskb.txt vs g3pA_taska.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g2pC_taskb.txt vs g3pB_taska.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g2pC_taskb.txt vs g4pD_taska.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g2pC_taskb.txt vs orig_taskc.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

g2pC_taskb.txt vs g0pA_taskc.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g2pC_taskb.txt vs g2pA_taska.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g2pC_taskb.txt vs g2pC_taskd.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g2pC_taskb.txt vs g4pD_taske.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g2pC_taskb.txt vs g4pD_taskd.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g2pC_taskb.txt vs g0pB_taska.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g2pC_taskb.txt vs g1pB_taske.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g2pC_taskb.txt vs g2pA_taskb.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

g2pC_taskb.txt vs g2pA_taskc.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

g2pC_taskb.txt vs g1pD_taska.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g2pC_taskb.txt vs g2pB_taska.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g2pC_taskb.txt vs g2pE_taskb.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g2pC_taskb.txt vs g4pE_taskc.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g2pC_taskb.txt vs g0pD_taskd.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g2pC_taskb.txt vs g0pE_taskd.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g2pC_taskb.txt vs g1pA_taskb.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g2pC_taskb.txt vs g1pB_taskb.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g2pC_taskb.txt vs g4pE_taskd.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g2pC_taskb.txt vs g2pC_taska.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g2pC_taskb.txt vs g2pC_taskc.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g2pC_taskb.txt vs g2pE_taska.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

g2pC_taskb.txt vs orig_taske.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

g2pC_taskb.txt vs g0pB_taskc.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

The vector space model has the following limitations:

g2pC_taskb.txt vs g0pC_taskd.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g2pC_taskb.txt vs g0pC_taske.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g2pC_taskb.txt vs g0pD_taskc.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g2pC_taskb.txt vs g0pC_taskb.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g2pC_taskb.txt vs g2pE_taske.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g2pC_taskb.txt vs g0pC_taska.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g2pC_taskb.txt vs g0pD_taska.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g2pC_taskb.txt vs g4pC_taska.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g2pC_taskb.txt vs g1pB_taskc.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

g2pC_taskb.txt vs g1pD_taskc.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g2pC_taskb.txt vs g2pB_taske.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

g2pC_taskb.txt vs g2pE_taskc.txt

The PageRank is a recursive algorithm used by Google to determine which webpages are more important than others. The algorithm considers the importance of a webpage to be reflected by how many other webpages link to that page, and the importance of those pages.

For each page that links to a page A, the PageRank between zero and one is calculated iteratively according to the following two key factors: The probability of a user navigating away from a page randomly; the PageRank of any page that links to A, divided by the total number of outbound links from that page. This assumes that a link among many outbound links is less valuable than a link among fewer outbound links. A variation of the PageRank method bases the importance of a webpage on how many visits the page gets. 

The method can be abused when people deliberately link to sites in order to raise a site's PageRank. However, it is still a good indicator for search engines to use as a variable in deciding on the most appropriate results according to a query.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g3pB_taskb.txt vs g3pB_taske.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

g3pB_taskb.txt vs g3pC_taskb.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

g3pB_taskb.txt vs g0pE_taske.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

g3pB_taskb.txt vs g1pB_taska.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

g3pB_taskb.txt vs g1pD_taskd.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

g3pB_taskb.txt vs g2pA_taskd.txt

g3pB_taskb.txt vs g3pC_taske.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

g3pB_taskb.txt vs g4pB_taskb.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

g3pB_taskb.txt vs g4pE_taske.txt

g3pB_taskb.txt vs g1pD_taskb.txt

g3pB_taskb.txt vs g3pC_taska.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

g3pB_taskb.txt vs g4pD_taskc.txt

g3pB_taskb.txt vs g4pE_taskb.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

g3pB_taskb.txt vs g0pB_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g3pB_taskb.txt vs g1pA_taska.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g3pB_taskb.txt vs g1pA_taske.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g3pB_taskb.txt vs g4pB_taske.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g3pB_taskb.txt vs g2pE_taskd.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g3pB_taskb.txt vs g4pB_taska.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g3pB_taskb.txt vs g4pB_taskd.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g3pB_taskb.txt vs g4pC_taskc.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g3pB_taskb.txt vs g0pE_taskb.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g3pB_taskb.txt vs g1pD_taske.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g3pB_taskb.txt vs g2pB_taskb.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g3pB_taskb.txt vs g2pB_taskd.txt

g3pB_taskb.txt vs g3pA_taske.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g3pB_taskb.txt vs g4pC_taskd.txt

g3pB_taskb.txt vs orig_taskb.txt

g3pB_taskb.txt vs g0pE_taskc.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g3pB_taskb.txt vs g2pB_taskc.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g3pB_taskb.txt vs g2pC_taske.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g3pB_taskb.txt vs g3pA_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g3pB_taskb.txt vs g1pA_taskc.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g3pB_taskb.txt vs g3pA_taskb.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g3pB_taskb.txt vs orig_taska.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g3pB_taskb.txt vs orig_taskd.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g3pB_taskb.txt vs g0pA_taskb.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g3pB_taskb.txt vs g0pB_taske.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g3pB_taskb.txt vs g0pD_taskb.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g3pB_taskb.txt vs g0pD_taske.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g3pB_taskb.txt vs g3pB_taskc.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g3pB_taskb.txt vs g3pC_taskc.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g3pB_taskb.txt vs g4pC_taskb.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g3pB_taskb.txt vs g4pC_taske.txt

g3pB_taskb.txt vs g0pA_taske.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g3pB_taskb.txt vs g0pE_taska.txt

g3pB_taskb.txt vs g3pA_taska.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g3pB_taskb.txt vs g3pB_taska.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g3pB_taskb.txt vs g4pD_taska.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g3pB_taskb.txt vs orig_taskc.txt

g3pB_taskb.txt vs g0pA_taskc.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g3pB_taskb.txt vs g2pA_taska.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g3pB_taskb.txt vs g2pC_taskd.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g3pB_taskb.txt vs g4pD_taske.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g3pB_taskb.txt vs g4pD_taskd.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g3pB_taskb.txt vs g0pB_taska.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g3pB_taskb.txt vs g1pB_taske.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g3pB_taskb.txt vs g2pA_taskb.txt

g3pB_taskb.txt vs g2pA_taskc.txt

g3pB_taskb.txt vs g1pD_taska.txt

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g3pB_taskb.txt vs g2pB_taska.txt

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g3pB_taskb.txt vs g2pE_taskb.txt

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g3pB_taskb.txt vs g4pE_taskc.txt

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g3pB_taskb.txt vs g0pD_taskd.txt

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g3pB_taskb.txt vs g0pE_taskd.txt

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g3pB_taskb.txt vs g1pA_taskb.txt

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g3pB_taskb.txt vs g1pB_taskb.txt

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g3pB_taskb.txt vs g4pE_taskd.txt

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g3pB_taskb.txt vs g2pC_taska.txt

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g3pB_taskb.txt vs g2pC_taskc.txt

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g3pB_taskb.txt vs g2pE_taska.txt

g3pB_taskb.txt vs orig_taske.txt

g3pB_taskb.txt vs g0pB_taskc.txt

The vector space model has the following limitations:

g3pB_taskb.txt vs g0pC_taskd.txt

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g3pB_taskb.txt vs g0pC_taske.txt

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g3pB_taskb.txt vs g0pD_taskc.txt

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g3pB_taskb.txt vs g0pC_taskb.txt

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g3pB_taskb.txt vs g2pE_taske.txt

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g3pB_taskb.txt vs g0pC_taska.txt

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g3pB_taskb.txt vs g0pD_taska.txt

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g3pB_taskb.txt vs g4pC_taska.txt

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g3pB_taskb.txt vs g1pB_taskc.txt

g3pB_taskb.txt vs g1pD_taskc.txt

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g3pB_taskb.txt vs g2pB_taske.txt

g3pB_taskb.txt vs g2pE_taskc.txt

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g3pB_taske.txt vs g3pC_taskb.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

g3pB_taske.txt vs g0pE_taske.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

g3pB_taske.txt vs g1pB_taska.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

g3pB_taske.txt vs g1pD_taskd.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

g3pB_taske.txt vs g2pA_taskd.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

g3pB_taske.txt vs g3pC_taske.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

g3pB_taske.txt vs g4pB_taskb.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

g3pB_taske.txt vs g4pE_taske.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

g3pB_taske.txt vs g1pD_taskb.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

g3pB_taske.txt vs g3pC_taska.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

g3pB_taske.txt vs g4pD_taskc.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

g3pB_taske.txt vs g4pE_taskb.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

g3pB_taske.txt vs g0pB_taskd.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g3pB_taske.txt vs g1pA_taska.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g3pB_taske.txt vs g1pA_taske.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g3pB_taske.txt vs g4pB_taske.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g3pB_taske.txt vs g2pE_taskd.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g3pB_taske.txt vs g4pB_taska.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g3pB_taske.txt vs g4pB_taskd.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g3pB_taske.txt vs g4pC_taskc.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g3pB_taske.txt vs g0pE_taskb.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g3pB_taske.txt vs g1pD_taske.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g3pB_taske.txt vs g2pB_taskb.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g3pB_taske.txt vs g2pB_taskd.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

g3pB_taske.txt vs g3pA_taske.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g3pB_taske.txt vs g4pC_taskd.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

g3pB_taske.txt vs orig_taskb.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

g3pB_taske.txt vs g0pE_taskc.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g3pB_taske.txt vs g2pB_taskc.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g3pB_taske.txt vs g2pC_taske.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g3pB_taske.txt vs g3pA_taskd.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g3pB_taske.txt vs g1pA_taskc.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g3pB_taske.txt vs g3pA_taskb.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g3pB_taske.txt vs orig_taska.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g3pB_taske.txt vs orig_taskd.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g3pB_taske.txt vs g0pA_taskb.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g3pB_taske.txt vs g0pB_taske.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g3pB_taske.txt vs g0pD_taskb.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g3pB_taske.txt vs g0pD_taske.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g3pB_taske.txt vs g3pB_taskc.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g3pB_taske.txt vs g3pC_taskc.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g3pB_taske.txt vs g4pC_taskb.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g3pB_taske.txt vs g4pC_taske.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

g3pB_taske.txt vs g0pA_taske.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g3pB_taske.txt vs g0pE_taska.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

g3pB_taske.txt vs g3pA_taska.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g3pB_taske.txt vs g3pB_taska.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g3pB_taske.txt vs g4pD_taska.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g3pB_taske.txt vs orig_taskc.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

g3pB_taske.txt vs g0pA_taskc.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g3pB_taske.txt vs g2pA_taska.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g3pB_taske.txt vs g2pC_taskd.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g3pB_taske.txt vs g4pD_taske.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g3pB_taske.txt vs g4pD_taskd.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g3pB_taske.txt vs g0pB_taska.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g3pB_taske.txt vs g1pB_taske.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g3pB_taske.txt vs g2pA_taskb.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

g3pB_taske.txt vs g2pA_taskc.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

g3pB_taske.txt vs g1pD_taska.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g3pB_taske.txt vs g2pB_taska.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g3pB_taske.txt vs g2pE_taskb.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g3pB_taske.txt vs g4pE_taskc.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g3pB_taske.txt vs g0pD_taskd.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g3pB_taske.txt vs g0pE_taskd.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g3pB_taske.txt vs g1pA_taskb.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g3pB_taske.txt vs g1pB_taskb.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g3pB_taske.txt vs g4pE_taskd.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g3pB_taske.txt vs g2pC_taska.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g3pB_taske.txt vs g2pC_taskc.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g3pB_taske.txt vs g2pE_taska.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

g3pB_taske.txt vs orig_taske.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

g3pB_taske.txt vs g0pB_taskc.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

The vector space model has the following limitations:

g3pB_taske.txt vs g0pC_taskd.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g3pB_taske.txt vs g0pC_taske.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g3pB_taske.txt vs g0pD_taskc.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g3pB_taske.txt vs g0pC_taskb.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g3pB_taske.txt vs g2pE_taske.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g3pB_taske.txt vs g0pC_taska.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g3pB_taske.txt vs g0pD_taska.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g3pB_taske.txt vs g4pC_taska.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g3pB_taske.txt vs g1pB_taskc.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

g3pB_taske.txt vs g1pD_taskc.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g3pB_taske.txt vs g2pB_taske.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

g3pB_taske.txt vs g2pE_taskc.txt

Dynamic Programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.  The term was originally used in the 1940s by Richard Bellman.

The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization.  The "program" is the optimal plan for action that is produced.

For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action. 

To say that a problem has overlapping subproblems is to say that the same subproblems are used to solve many different larger problems.  Optimal substructure means that optimal solutions of subproblems can be used to find the optimal solutions of the overall problem.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g3pC_taskb.txt vs g0pE_taske.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

g3pC_taskb.txt vs g1pB_taska.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

g3pC_taskb.txt vs g1pD_taskd.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

g3pC_taskb.txt vs g2pA_taskd.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

g3pC_taskb.txt vs g3pC_taske.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

g3pC_taskb.txt vs g4pB_taskb.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

g3pC_taskb.txt vs g4pE_taske.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

g3pC_taskb.txt vs g1pD_taskb.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

g3pC_taskb.txt vs g3pC_taska.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

g3pC_taskb.txt vs g4pD_taskc.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

g3pC_taskb.txt vs g4pE_taskb.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

g3pC_taskb.txt vs g0pB_taskd.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g3pC_taskb.txt vs g1pA_taska.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g3pC_taskb.txt vs g1pA_taske.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g3pC_taskb.txt vs g4pB_taske.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g3pC_taskb.txt vs g2pE_taskd.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g3pC_taskb.txt vs g4pB_taska.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g3pC_taskb.txt vs g4pB_taskd.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g3pC_taskb.txt vs g4pC_taskc.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g3pC_taskb.txt vs g0pE_taskb.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g3pC_taskb.txt vs g1pD_taske.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g3pC_taskb.txt vs g2pB_taskb.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g3pC_taskb.txt vs g2pB_taskd.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

g3pC_taskb.txt vs g3pA_taske.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g3pC_taskb.txt vs g4pC_taskd.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

g3pC_taskb.txt vs orig_taskb.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

g3pC_taskb.txt vs g0pE_taskc.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g3pC_taskb.txt vs g2pB_taskc.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g3pC_taskb.txt vs g2pC_taske.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g3pC_taskb.txt vs g3pA_taskd.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g3pC_taskb.txt vs g1pA_taskc.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g3pC_taskb.txt vs g3pA_taskb.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g3pC_taskb.txt vs orig_taska.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g3pC_taskb.txt vs orig_taskd.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g3pC_taskb.txt vs g0pA_taskb.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g3pC_taskb.txt vs g0pB_taske.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g3pC_taskb.txt vs g0pD_taskb.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g3pC_taskb.txt vs g0pD_taske.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g3pC_taskb.txt vs g3pB_taskc.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g3pC_taskb.txt vs g3pC_taskc.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g3pC_taskb.txt vs g4pC_taskb.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g3pC_taskb.txt vs g4pC_taske.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

g3pC_taskb.txt vs g0pA_taske.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g3pC_taskb.txt vs g0pE_taska.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

g3pC_taskb.txt vs g3pA_taska.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g3pC_taskb.txt vs g3pB_taska.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g3pC_taskb.txt vs g4pD_taska.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g3pC_taskb.txt vs orig_taskc.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

g3pC_taskb.txt vs g0pA_taskc.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g3pC_taskb.txt vs g2pA_taska.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g3pC_taskb.txt vs g2pC_taskd.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g3pC_taskb.txt vs g4pD_taske.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g3pC_taskb.txt vs g4pD_taskd.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g3pC_taskb.txt vs g0pB_taska.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g3pC_taskb.txt vs g1pB_taske.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g3pC_taskb.txt vs g2pA_taskb.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

g3pC_taskb.txt vs g2pA_taskc.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

g3pC_taskb.txt vs g1pD_taska.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g3pC_taskb.txt vs g2pB_taska.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g3pC_taskb.txt vs g2pE_taskb.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g3pC_taskb.txt vs g4pE_taskc.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g3pC_taskb.txt vs g0pD_taskd.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g3pC_taskb.txt vs g0pE_taskd.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g3pC_taskb.txt vs g1pA_taskb.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g3pC_taskb.txt vs g1pB_taskb.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g3pC_taskb.txt vs g4pE_taskd.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g3pC_taskb.txt vs g2pC_taska.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g3pC_taskb.txt vs g2pC_taskc.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g3pC_taskb.txt vs g2pE_taska.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

g3pC_taskb.txt vs orig_taske.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

g3pC_taskb.txt vs g0pB_taskc.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

The vector space model has the following limitations:

g3pC_taskb.txt vs g0pC_taskd.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g3pC_taskb.txt vs g0pC_taske.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g3pC_taskb.txt vs g0pD_taskc.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g3pC_taskb.txt vs g0pC_taskb.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g3pC_taskb.txt vs g2pE_taske.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g3pC_taskb.txt vs g0pC_taska.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g3pC_taskb.txt vs g0pD_taska.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g3pC_taskb.txt vs g4pC_taska.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g3pC_taskb.txt vs g1pB_taskc.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

g3pC_taskb.txt vs g1pD_taskc.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g3pC_taskb.txt vs g2pB_taske.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

g3pC_taskb.txt vs g2pE_taskc.txt

The PageRank algorithm used by google harnesses the implicit collective
intelligence present in the structure of the world wide web. Any page on
the Internet will generally link to at least one other, by modelling this
link structure as a graph, we can build up a symbolic representation of
the world wide web.

As the basic level, the nodes with the highest degrees can be considered
the most "popular" and by inference the most important - which can be used
to rank the pages when returning search results.

Expanding on this theory, we can then say that the links from an important
pages are themselves more important. Using this idea we can adjust the
rankings of our pages so that pages linked to be the most important pages
are considered more relevant.

The actual Google PageRank algorithm is much more complex than this, but
follows the same underlying principles. It incorporates some more advanced
reasoning to avoid website creators exploiting their knowledge of the algorithm
to artificially increase their PageRank through use of web-rings and other
similar reciprocal hyperlinking schemes.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g0pE_taske.txt vs g1pB_taska.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

g0pE_taske.txt vs g1pD_taskd.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

g0pE_taske.txt vs g2pA_taskd.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

g0pE_taske.txt vs g3pC_taske.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

g0pE_taske.txt vs g4pB_taskb.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

g0pE_taske.txt vs g4pE_taske.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

g0pE_taske.txt vs g1pD_taskb.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

g0pE_taske.txt vs g3pC_taska.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

g0pE_taske.txt vs g4pD_taskc.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

g0pE_taske.txt vs g4pE_taskb.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

g0pE_taske.txt vs g0pB_taskd.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g0pE_taske.txt vs g1pA_taska.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g0pE_taske.txt vs g1pA_taske.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g0pE_taske.txt vs g4pB_taske.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g0pE_taske.txt vs g2pE_taskd.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g0pE_taske.txt vs g4pB_taska.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g0pE_taske.txt vs g4pB_taskd.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g0pE_taske.txt vs g4pC_taskc.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g0pE_taske.txt vs g0pE_taskb.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g0pE_taske.txt vs g1pD_taske.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g0pE_taske.txt vs g2pB_taskb.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g0pE_taske.txt vs g2pB_taskd.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

g0pE_taske.txt vs g3pA_taske.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g0pE_taske.txt vs g4pC_taskd.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

g0pE_taske.txt vs orig_taskb.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

g0pE_taske.txt vs g0pE_taskc.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g0pE_taske.txt vs g2pB_taskc.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g0pE_taske.txt vs g2pC_taske.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g0pE_taske.txt vs g3pA_taskd.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g0pE_taske.txt vs g1pA_taskc.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g0pE_taske.txt vs g3pA_taskb.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g0pE_taske.txt vs orig_taska.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g0pE_taske.txt vs orig_taskd.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g0pE_taske.txt vs g0pA_taskb.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g0pE_taske.txt vs g0pB_taske.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g0pE_taske.txt vs g0pD_taskb.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g0pE_taske.txt vs g0pD_taske.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g0pE_taske.txt vs g3pB_taskc.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g0pE_taske.txt vs g3pC_taskc.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g0pE_taske.txt vs g4pC_taskb.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g0pE_taske.txt vs g4pC_taske.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

g0pE_taske.txt vs g0pA_taske.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g0pE_taske.txt vs g0pE_taska.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

g0pE_taske.txt vs g3pA_taska.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g0pE_taske.txt vs g3pB_taska.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g0pE_taske.txt vs g4pD_taska.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g0pE_taske.txt vs orig_taskc.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

g0pE_taske.txt vs g0pA_taskc.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g0pE_taske.txt vs g2pA_taska.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g0pE_taske.txt vs g2pC_taskd.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g0pE_taske.txt vs g4pD_taske.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g0pE_taske.txt vs g4pD_taskd.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g0pE_taske.txt vs g0pB_taska.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g0pE_taske.txt vs g1pB_taske.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g0pE_taske.txt vs g2pA_taskb.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

g0pE_taske.txt vs g2pA_taskc.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

g0pE_taske.txt vs g1pD_taska.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g0pE_taske.txt vs g2pB_taska.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g0pE_taske.txt vs g2pE_taskb.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g0pE_taske.txt vs g4pE_taskc.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g0pE_taske.txt vs g0pD_taskd.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g0pE_taske.txt vs g0pE_taskd.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g0pE_taske.txt vs g1pA_taskb.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g0pE_taske.txt vs g1pB_taskb.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g0pE_taske.txt vs g4pE_taskd.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g0pE_taske.txt vs g2pC_taska.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g0pE_taske.txt vs g2pC_taskc.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g0pE_taske.txt vs g2pE_taska.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

g0pE_taske.txt vs orig_taske.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

g0pE_taske.txt vs g0pB_taskc.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

The vector space model has the following limitations:

g0pE_taske.txt vs g0pC_taskd.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g0pE_taske.txt vs g0pC_taske.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g0pE_taske.txt vs g0pD_taskc.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g0pE_taske.txt vs g0pC_taskb.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g0pE_taske.txt vs g2pE_taske.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g0pE_taske.txt vs g0pC_taska.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g0pE_taske.txt vs g0pD_taska.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g0pE_taske.txt vs g4pC_taska.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g0pE_taske.txt vs g1pB_taskc.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

g0pE_taske.txt vs g1pD_taskc.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g0pE_taske.txt vs g2pB_taske.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

g0pE_taske.txt vs g2pE_taskc.txt

dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure (described below). The method takes much less time than naive methods. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g1pB_taska.txt vs g1pD_taskd.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

g1pB_taska.txt vs g2pA_taskd.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

g1pB_taska.txt vs g3pC_taske.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

g1pB_taska.txt vs g4pB_taskb.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

g1pB_taska.txt vs g4pE_taske.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

g1pB_taska.txt vs g1pD_taskb.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

g1pB_taska.txt vs g3pC_taska.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

g1pB_taska.txt vs g4pD_taskc.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

g1pB_taska.txt vs g4pE_taskb.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
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g1pB_taska.txt vs g0pB_taskd.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g1pB_taska.txt vs g1pA_taska.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g1pB_taska.txt vs g1pA_taske.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g1pB_taska.txt vs g4pB_taske.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g1pB_taska.txt vs g2pE_taskd.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g1pB_taska.txt vs g4pB_taska.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g1pB_taska.txt vs g4pB_taskd.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g1pB_taska.txt vs g4pC_taskc.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g1pB_taska.txt vs g0pE_taskb.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g1pB_taska.txt vs g1pD_taske.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g1pB_taska.txt vs g2pB_taskb.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g1pB_taska.txt vs g2pB_taskd.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

g1pB_taska.txt vs g3pA_taske.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g1pB_taska.txt vs g4pC_taskd.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

g1pB_taska.txt vs orig_taskb.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

g1pB_taska.txt vs g0pE_taskc.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g1pB_taska.txt vs g2pB_taskc.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g1pB_taska.txt vs g2pC_taske.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g1pB_taska.txt vs g3pA_taskd.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g1pB_taska.txt vs g1pA_taskc.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g1pB_taska.txt vs g3pA_taskb.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g1pB_taska.txt vs orig_taska.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g1pB_taska.txt vs orig_taskd.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g1pB_taska.txt vs g0pA_taskb.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g1pB_taska.txt vs g0pB_taske.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g1pB_taska.txt vs g0pD_taskb.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g1pB_taska.txt vs g0pD_taske.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g1pB_taska.txt vs g3pB_taskc.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g1pB_taska.txt vs g3pC_taskc.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g1pB_taska.txt vs g4pC_taskb.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g1pB_taska.txt vs g4pC_taske.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

g1pB_taska.txt vs g0pA_taske.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g1pB_taska.txt vs g0pE_taska.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

g1pB_taska.txt vs g3pA_taska.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g1pB_taska.txt vs g3pB_taska.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g1pB_taska.txt vs g4pD_taska.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g1pB_taska.txt vs orig_taskc.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

g1pB_taska.txt vs g0pA_taskc.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g1pB_taska.txt vs g2pA_taska.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g1pB_taska.txt vs g2pC_taskd.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g1pB_taska.txt vs g4pD_taske.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g1pB_taska.txt vs g4pD_taskd.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g1pB_taska.txt vs g0pB_taska.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g1pB_taska.txt vs g1pB_taske.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g1pB_taska.txt vs g2pA_taskb.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

g1pB_taska.txt vs g2pA_taskc.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

g1pB_taska.txt vs g1pD_taska.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g1pB_taska.txt vs g2pB_taska.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g1pB_taska.txt vs g2pE_taskb.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g1pB_taska.txt vs g4pE_taskc.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g1pB_taska.txt vs g0pD_taskd.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g1pB_taska.txt vs g0pE_taskd.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g1pB_taska.txt vs g1pA_taskb.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g1pB_taska.txt vs g1pB_taskb.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g1pB_taska.txt vs g4pE_taskd.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g1pB_taska.txt vs g2pC_taska.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g1pB_taska.txt vs g2pC_taskc.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g1pB_taska.txt vs g2pE_taska.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

g1pB_taska.txt vs orig_taske.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

g1pB_taska.txt vs g0pB_taskc.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

The vector space model has the following limitations:

g1pB_taska.txt vs g0pC_taskd.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g1pB_taska.txt vs g0pC_taske.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g1pB_taska.txt vs g0pD_taskc.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g1pB_taska.txt vs g0pC_taskb.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g1pB_taska.txt vs g2pE_taske.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g1pB_taska.txt vs g0pC_taska.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g1pB_taska.txt vs g0pD_taska.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g1pB_taska.txt vs g4pC_taska.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g1pB_taska.txt vs g1pB_taskc.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

g1pB_taska.txt vs g1pD_taskc.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g1pB_taska.txt vs g2pB_taske.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

g1pB_taska.txt vs g2pE_taskc.txt

Inheritance is one of the basic concepts of Object Oriented Programming.  It�s objective is to add more detail to pre-existing classes whilst still allowing the methods and variables of these classes to be reused.  The easiest way to look at inheritance is as an ��is a kind of� relationship.  For example, a guitar is a kind of string instrument, electric, acoustic and steel stringed are all types of guitar.
The further down an inheritance tree you get, the more specific the classes become.  An example here would be books.  Books generally fall into two categories, fiction and non-fiction.  Each of these can then be sub-divided into more groups.  Fiction for example can be split into fantasy, horror, romance and many more.  Non-fiction splits the same way into other topics such as history, geography, cooking etc.  History of course can be sub-divided into time periods like the Romans, the Elizabethans, the World Wars and so on.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g1pD_taskd.txt vs g2pA_taskd.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

g1pD_taskd.txt vs g3pC_taske.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

g1pD_taskd.txt vs g4pB_taskb.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

g1pD_taskd.txt vs g4pE_taske.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

g1pD_taskd.txt vs g1pD_taskb.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

g1pD_taskd.txt vs g3pC_taska.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

g1pD_taskd.txt vs g4pD_taskc.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

g1pD_taskd.txt vs g4pE_taskb.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
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g1pD_taskd.txt vs g0pB_taskd.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g1pD_taskd.txt vs g1pA_taska.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g1pD_taskd.txt vs g1pA_taske.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g1pD_taskd.txt vs g4pB_taske.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g1pD_taskd.txt vs g2pE_taskd.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g1pD_taskd.txt vs g4pB_taska.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g1pD_taskd.txt vs g4pB_taskd.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g1pD_taskd.txt vs g4pC_taskc.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g1pD_taskd.txt vs g0pE_taskb.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g1pD_taskd.txt vs g1pD_taske.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g1pD_taskd.txt vs g2pB_taskb.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g1pD_taskd.txt vs g2pB_taskd.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

g1pD_taskd.txt vs g3pA_taske.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g1pD_taskd.txt vs g4pC_taskd.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

g1pD_taskd.txt vs orig_taskb.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

g1pD_taskd.txt vs g0pE_taskc.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g1pD_taskd.txt vs g2pB_taskc.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g1pD_taskd.txt vs g2pC_taske.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g1pD_taskd.txt vs g3pA_taskd.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g1pD_taskd.txt vs g1pA_taskc.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g1pD_taskd.txt vs g3pA_taskb.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g1pD_taskd.txt vs orig_taska.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g1pD_taskd.txt vs orig_taskd.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g1pD_taskd.txt vs g0pA_taskb.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g1pD_taskd.txt vs g0pB_taske.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g1pD_taskd.txt vs g0pD_taskb.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g1pD_taskd.txt vs g0pD_taske.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g1pD_taskd.txt vs g3pB_taskc.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g1pD_taskd.txt vs g3pC_taskc.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g1pD_taskd.txt vs g4pC_taskb.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g1pD_taskd.txt vs g4pC_taske.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

g1pD_taskd.txt vs g0pA_taske.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g1pD_taskd.txt vs g0pE_taska.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

g1pD_taskd.txt vs g3pA_taska.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g1pD_taskd.txt vs g3pB_taska.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g1pD_taskd.txt vs g4pD_taska.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g1pD_taskd.txt vs orig_taskc.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

g1pD_taskd.txt vs g0pA_taskc.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g1pD_taskd.txt vs g2pA_taska.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g1pD_taskd.txt vs g2pC_taskd.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g1pD_taskd.txt vs g4pD_taske.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g1pD_taskd.txt vs g4pD_taskd.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g1pD_taskd.txt vs g0pB_taska.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g1pD_taskd.txt vs g1pB_taske.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g1pD_taskd.txt vs g2pA_taskb.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

g1pD_taskd.txt vs g2pA_taskc.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

g1pD_taskd.txt vs g1pD_taska.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g1pD_taskd.txt vs g2pB_taska.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g1pD_taskd.txt vs g2pE_taskb.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g1pD_taskd.txt vs g4pE_taskc.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g1pD_taskd.txt vs g0pD_taskd.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g1pD_taskd.txt vs g0pE_taskd.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g1pD_taskd.txt vs g1pA_taskb.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g1pD_taskd.txt vs g1pB_taskb.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g1pD_taskd.txt vs g4pE_taskd.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g1pD_taskd.txt vs g2pC_taska.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g1pD_taskd.txt vs g2pC_taskc.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g1pD_taskd.txt vs g2pE_taska.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

g1pD_taskd.txt vs orig_taske.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

g1pD_taskd.txt vs g0pB_taskc.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

The vector space model has the following limitations:

g1pD_taskd.txt vs g0pC_taskd.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g1pD_taskd.txt vs g0pC_taske.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g1pD_taskd.txt vs g0pD_taskc.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g1pD_taskd.txt vs g0pC_taskb.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g1pD_taskd.txt vs g2pE_taske.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g1pD_taskd.txt vs g0pC_taska.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g1pD_taskd.txt vs g0pD_taska.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g1pD_taskd.txt vs g4pC_taska.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g1pD_taskd.txt vs g1pB_taskc.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

g1pD_taskd.txt vs g1pD_taskc.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g1pD_taskd.txt vs g2pB_taske.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

g1pD_taskd.txt vs g2pE_taskc.txt

Bayes Theorem is a mathematical formula used to calculate conditional probabilities. Given the probability of event A given event B, Bayes Theorem can be used to calculate the probability of B given A.  This is achieved using the conditional probability of B given A and the prior probabilities of both events A and B. For example: suppose there is a bag of coloured balls with 25 red ones and 75 black ones. Lucky Joe likes to predict the colour of the ball he selects and he is 80% accurate. Joe records all of his results and about 0.5% of the time he accidently records the wrong results. Using all of this information more probabilities can be inferred, including using Bayes Theorem to calculate various probabilities like Joe recording correctly if he guesses correctly or Joe recording incorrectly when his guess was correct (and other like combinations).

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g2pA_taskd.txt vs g3pC_taske.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

g2pA_taskd.txt vs g4pB_taskb.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

g2pA_taskd.txt vs g4pE_taske.txt

g2pA_taskd.txt vs g1pD_taskb.txt

g2pA_taskd.txt vs g3pC_taska.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

g2pA_taskd.txt vs g4pD_taskc.txt

g2pA_taskd.txt vs g4pE_taskb.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

g2pA_taskd.txt vs g0pB_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g2pA_taskd.txt vs g1pA_taska.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g2pA_taskd.txt vs g1pA_taske.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g2pA_taskd.txt vs g4pB_taske.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g2pA_taskd.txt vs g2pE_taskd.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g2pA_taskd.txt vs g4pB_taska.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g2pA_taskd.txt vs g4pB_taskd.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g2pA_taskd.txt vs g4pC_taskc.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g2pA_taskd.txt vs g0pE_taskb.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g2pA_taskd.txt vs g1pD_taske.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g2pA_taskd.txt vs g2pB_taskb.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g2pA_taskd.txt vs g2pB_taskd.txt

g2pA_taskd.txt vs g3pA_taske.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g2pA_taskd.txt vs g4pC_taskd.txt

g2pA_taskd.txt vs orig_taskb.txt

g2pA_taskd.txt vs g0pE_taskc.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g2pA_taskd.txt vs g2pB_taskc.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g2pA_taskd.txt vs g2pC_taske.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g2pA_taskd.txt vs g3pA_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g2pA_taskd.txt vs g1pA_taskc.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g2pA_taskd.txt vs g3pA_taskb.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g2pA_taskd.txt vs orig_taska.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g2pA_taskd.txt vs orig_taskd.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g2pA_taskd.txt vs g0pA_taskb.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g2pA_taskd.txt vs g0pB_taske.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g2pA_taskd.txt vs g0pD_taskb.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g2pA_taskd.txt vs g0pD_taske.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g2pA_taskd.txt vs g3pB_taskc.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g2pA_taskd.txt vs g3pC_taskc.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g2pA_taskd.txt vs g4pC_taskb.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g2pA_taskd.txt vs g4pC_taske.txt

g2pA_taskd.txt vs g0pA_taske.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g2pA_taskd.txt vs g0pE_taska.txt

g2pA_taskd.txt vs g3pA_taska.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g2pA_taskd.txt vs g3pB_taska.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g2pA_taskd.txt vs g4pD_taska.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g2pA_taskd.txt vs orig_taskc.txt

g2pA_taskd.txt vs g0pA_taskc.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g2pA_taskd.txt vs g2pA_taska.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g2pA_taskd.txt vs g2pC_taskd.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g2pA_taskd.txt vs g4pD_taske.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g2pA_taskd.txt vs g4pD_taskd.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g2pA_taskd.txt vs g0pB_taska.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g2pA_taskd.txt vs g1pB_taske.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g2pA_taskd.txt vs g2pA_taskb.txt

g2pA_taskd.txt vs g2pA_taskc.txt

g2pA_taskd.txt vs g1pD_taska.txt

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g2pA_taskd.txt vs g2pB_taska.txt

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g2pA_taskd.txt vs g2pE_taskb.txt

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g2pA_taskd.txt vs g4pE_taskc.txt

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g2pA_taskd.txt vs g0pD_taskd.txt

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g2pA_taskd.txt vs g0pE_taskd.txt

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g2pA_taskd.txt vs g1pA_taskb.txt

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g2pA_taskd.txt vs g1pB_taskb.txt

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g2pA_taskd.txt vs g4pE_taskd.txt

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g2pA_taskd.txt vs g2pC_taska.txt

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g2pA_taskd.txt vs g2pC_taskc.txt

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g2pA_taskd.txt vs g2pE_taska.txt

g2pA_taskd.txt vs orig_taske.txt

g2pA_taskd.txt vs g0pB_taskc.txt

The vector space model has the following limitations:

g2pA_taskd.txt vs g0pC_taskd.txt

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g2pA_taskd.txt vs g0pC_taske.txt

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g2pA_taskd.txt vs g0pD_taskc.txt

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g2pA_taskd.txt vs g0pC_taskb.txt

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g2pA_taskd.txt vs g2pE_taske.txt

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g2pA_taskd.txt vs g0pC_taska.txt

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g2pA_taskd.txt vs g0pD_taska.txt

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g2pA_taskd.txt vs g4pC_taska.txt

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g2pA_taskd.txt vs g1pB_taskc.txt

g2pA_taskd.txt vs g1pD_taskc.txt

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g2pA_taskd.txt vs g2pB_taske.txt

g2pA_taskd.txt vs g2pE_taskc.txt

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g3pC_taske.txt vs g4pB_taskb.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

g3pC_taske.txt vs g4pE_taske.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

g3pC_taske.txt vs g1pD_taskb.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

g3pC_taske.txt vs g3pC_taska.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

g3pC_taske.txt vs g4pD_taskc.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

g3pC_taske.txt vs g4pE_taskb.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

g3pC_taske.txt vs g0pB_taskd.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g3pC_taske.txt vs g1pA_taska.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g3pC_taske.txt vs g1pA_taske.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g3pC_taske.txt vs g4pB_taske.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g3pC_taske.txt vs g2pE_taskd.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g3pC_taske.txt vs g4pB_taska.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g3pC_taske.txt vs g4pB_taskd.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g3pC_taske.txt vs g4pC_taskc.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g3pC_taske.txt vs g0pE_taskb.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g3pC_taske.txt vs g1pD_taske.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g3pC_taske.txt vs g2pB_taskb.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g3pC_taske.txt vs g2pB_taskd.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

g3pC_taske.txt vs g3pA_taske.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g3pC_taske.txt vs g4pC_taskd.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

g3pC_taske.txt vs orig_taskb.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

g3pC_taske.txt vs g0pE_taskc.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g3pC_taske.txt vs g2pB_taskc.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g3pC_taske.txt vs g2pC_taske.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g3pC_taske.txt vs g3pA_taskd.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g3pC_taske.txt vs g1pA_taskc.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g3pC_taske.txt vs g3pA_taskb.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g3pC_taske.txt vs orig_taska.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g3pC_taske.txt vs orig_taskd.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g3pC_taske.txt vs g0pA_taskb.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g3pC_taske.txt vs g0pB_taske.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g3pC_taske.txt vs g0pD_taskb.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g3pC_taske.txt vs g0pD_taske.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g3pC_taske.txt vs g3pB_taskc.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g3pC_taske.txt vs g3pC_taskc.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g3pC_taske.txt vs g4pC_taskb.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g3pC_taske.txt vs g4pC_taske.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

g3pC_taske.txt vs g0pA_taske.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g3pC_taske.txt vs g0pE_taska.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

g3pC_taske.txt vs g3pA_taska.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g3pC_taske.txt vs g3pB_taska.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g3pC_taske.txt vs g4pD_taska.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g3pC_taske.txt vs orig_taskc.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

g3pC_taske.txt vs g0pA_taskc.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g3pC_taske.txt vs g2pA_taska.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g3pC_taske.txt vs g2pC_taskd.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g3pC_taske.txt vs g4pD_taske.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g3pC_taske.txt vs g4pD_taskd.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g3pC_taske.txt vs g0pB_taska.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g3pC_taske.txt vs g1pB_taske.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g3pC_taske.txt vs g2pA_taskb.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

g3pC_taske.txt vs g2pA_taskc.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

g3pC_taske.txt vs g1pD_taska.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g3pC_taske.txt vs g2pB_taska.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g3pC_taske.txt vs g2pE_taskb.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g3pC_taske.txt vs g4pE_taskc.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g3pC_taske.txt vs g0pD_taskd.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g3pC_taske.txt vs g0pE_taskd.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g3pC_taske.txt vs g1pA_taskb.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g3pC_taske.txt vs g1pB_taskb.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g3pC_taske.txt vs g4pE_taskd.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g3pC_taske.txt vs g2pC_taska.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g3pC_taske.txt vs g2pC_taskc.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g3pC_taske.txt vs g2pE_taska.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

g3pC_taske.txt vs orig_taske.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

g3pC_taske.txt vs g0pB_taskc.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

The vector space model has the following limitations:

g3pC_taske.txt vs g0pC_taskd.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g3pC_taske.txt vs g0pC_taske.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g3pC_taske.txt vs g0pD_taskc.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g3pC_taske.txt vs g0pC_taskb.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g3pC_taske.txt vs g2pE_taske.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g3pC_taske.txt vs g0pC_taska.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g3pC_taske.txt vs g0pD_taska.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g3pC_taske.txt vs g4pC_taska.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g3pC_taske.txt vs g1pB_taskc.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

g3pC_taske.txt vs g1pD_taskc.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g3pC_taske.txt vs g2pB_taske.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

g3pC_taske.txt vs g2pE_taskc.txt

In computer science and mathematics, dynamic programming
is a method of problem solving that utilises the properties
of overlapping subproblems and optimal substructure. And thus
the method takes much less time than more naive methods.

In "dynamic programming", the word "programming" has no
real connection to computer programming at all, it actually
comes from the term "mathematical programming",
a synonym for optimisation. Thus, the "program" is the optimal
plan of action that is being produced. For example, a
schedule of events at an exhibition is sometimes called a
programme. Programming, in this sense, means finding an
acceptable plan, an algorithm.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g4pB_taskb.txt vs g4pE_taske.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

g4pB_taskb.txt vs g1pD_taskb.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

g4pB_taskb.txt vs g3pC_taska.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

g4pB_taskb.txt vs g4pD_taskc.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

g4pB_taskb.txt vs g4pE_taskb.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
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g4pB_taskb.txt vs g0pB_taskd.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g4pB_taskb.txt vs g1pA_taska.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g4pB_taskb.txt vs g1pA_taske.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g4pB_taskb.txt vs g4pB_taske.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g4pB_taskb.txt vs g2pE_taskd.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g4pB_taskb.txt vs g4pB_taska.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g4pB_taskb.txt vs g4pB_taskd.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g4pB_taskb.txt vs g4pC_taskc.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g4pB_taskb.txt vs g0pE_taskb.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g4pB_taskb.txt vs g1pD_taske.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g4pB_taskb.txt vs g2pB_taskb.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g4pB_taskb.txt vs g2pB_taskd.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

g4pB_taskb.txt vs g3pA_taske.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g4pB_taskb.txt vs g4pC_taskd.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

g4pB_taskb.txt vs orig_taskb.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

g4pB_taskb.txt vs g0pE_taskc.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g4pB_taskb.txt vs g2pB_taskc.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g4pB_taskb.txt vs g2pC_taske.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g4pB_taskb.txt vs g3pA_taskd.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g4pB_taskb.txt vs g1pA_taskc.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g4pB_taskb.txt vs g3pA_taskb.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g4pB_taskb.txt vs orig_taska.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g4pB_taskb.txt vs orig_taskd.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g4pB_taskb.txt vs g0pA_taskb.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g4pB_taskb.txt vs g0pB_taske.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g4pB_taskb.txt vs g0pD_taskb.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g4pB_taskb.txt vs g0pD_taske.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g4pB_taskb.txt vs g3pB_taskc.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g4pB_taskb.txt vs g3pC_taskc.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g4pB_taskb.txt vs g4pC_taskb.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g4pB_taskb.txt vs g4pC_taske.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

g4pB_taskb.txt vs g0pA_taske.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g4pB_taskb.txt vs g0pE_taska.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

g4pB_taskb.txt vs g3pA_taska.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g4pB_taskb.txt vs g3pB_taska.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g4pB_taskb.txt vs g4pD_taska.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g4pB_taskb.txt vs orig_taskc.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

g4pB_taskb.txt vs g0pA_taskc.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g4pB_taskb.txt vs g2pA_taska.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g4pB_taskb.txt vs g2pC_taskd.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g4pB_taskb.txt vs g4pD_taske.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g4pB_taskb.txt vs g4pD_taskd.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g4pB_taskb.txt vs g0pB_taska.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g4pB_taskb.txt vs g1pB_taske.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g4pB_taskb.txt vs g2pA_taskb.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

g4pB_taskb.txt vs g2pA_taskc.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

g4pB_taskb.txt vs g1pD_taska.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g4pB_taskb.txt vs g2pB_taska.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g4pB_taskb.txt vs g2pE_taskb.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g4pB_taskb.txt vs g4pE_taskc.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g4pB_taskb.txt vs g0pD_taskd.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g4pB_taskb.txt vs g0pE_taskd.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g4pB_taskb.txt vs g1pA_taskb.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g4pB_taskb.txt vs g1pB_taskb.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g4pB_taskb.txt vs g4pE_taskd.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g4pB_taskb.txt vs g2pC_taska.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g4pB_taskb.txt vs g2pC_taskc.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g4pB_taskb.txt vs g2pE_taska.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

g4pB_taskb.txt vs orig_taske.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

g4pB_taskb.txt vs g0pB_taskc.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

The vector space model has the following limitations:

g4pB_taskb.txt vs g0pC_taskd.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g4pB_taskb.txt vs g0pC_taske.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g4pB_taskb.txt vs g0pD_taskc.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g4pB_taskb.txt vs g0pC_taskb.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g4pB_taskb.txt vs g2pE_taske.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g4pB_taskb.txt vs g0pC_taska.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g4pB_taskb.txt vs g0pD_taska.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g4pB_taskb.txt vs g4pC_taska.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g4pB_taskb.txt vs g1pB_taskc.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

g4pB_taskb.txt vs g1pD_taskc.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g4pB_taskb.txt vs g2pB_taske.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

g4pB_taskb.txt vs g2pE_taskc.txt

Page rank algorithm is used to determine a webpage�s importance or relevance in the web dependant on certain criteria. The criteria may include numbers of word matches with the search terms, number of other webpages that link this one and/or cite it as a source, number of unique visits for certain amount of time etc. There are some techniques that try to fool the search engines like link farms, keyword spamming and a lot of meta tags. The last two are somewhat easier to be dealt with (simply by being ignored most of the time). Link farms are groups of sites that are producing links between each other pursuing higher link counts. The reason for such manipulations is the pursuit of higher page rank so even higher number of users will see the page which will lead to higher income. Link farms can be exploited by joining to them and get inbound linkage but refuse to add links for one�s own site to the sites from the link farm. Google�s toolbar tries to follow the intentional user model by counting the visits from actual users (i.e. not computer bots) to a website. Page ranks can be calculated either recursively or iteratively. One of the most important uses of page rank is its meaning to advertising.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g4pE_taske.txt vs g1pD_taskb.txt

g4pE_taske.txt vs g3pC_taska.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

g4pE_taske.txt vs g4pD_taskc.txt

g4pE_taske.txt vs g4pE_taskb.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
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g4pE_taske.txt vs g0pB_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g4pE_taske.txt vs g1pA_taska.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g4pE_taske.txt vs g1pA_taske.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g4pE_taske.txt vs g4pB_taske.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g4pE_taske.txt vs g2pE_taskd.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g4pE_taske.txt vs g4pB_taska.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g4pE_taske.txt vs g4pB_taskd.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g4pE_taske.txt vs g4pC_taskc.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g4pE_taske.txt vs g0pE_taskb.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g4pE_taske.txt vs g1pD_taske.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g4pE_taske.txt vs g2pB_taskb.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g4pE_taske.txt vs g2pB_taskd.txt

g4pE_taske.txt vs g3pA_taske.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g4pE_taske.txt vs g4pC_taskd.txt

g4pE_taske.txt vs orig_taskb.txt

g4pE_taske.txt vs g0pE_taskc.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g4pE_taske.txt vs g2pB_taskc.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g4pE_taske.txt vs g2pC_taske.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g4pE_taske.txt vs g3pA_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g4pE_taske.txt vs g1pA_taskc.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g4pE_taske.txt vs g3pA_taskb.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g4pE_taske.txt vs orig_taska.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g4pE_taske.txt vs orig_taskd.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g4pE_taske.txt vs g0pA_taskb.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g4pE_taske.txt vs g0pB_taske.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g4pE_taske.txt vs g0pD_taskb.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g4pE_taske.txt vs g0pD_taske.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g4pE_taske.txt vs g3pB_taskc.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g4pE_taske.txt vs g3pC_taskc.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g4pE_taske.txt vs g4pC_taskb.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g4pE_taske.txt vs g4pC_taske.txt

g4pE_taske.txt vs g0pA_taske.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g4pE_taske.txt vs g0pE_taska.txt

g4pE_taske.txt vs g3pA_taska.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g4pE_taske.txt vs g3pB_taska.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g4pE_taske.txt vs g4pD_taska.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g4pE_taske.txt vs orig_taskc.txt

g4pE_taske.txt vs g0pA_taskc.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g4pE_taske.txt vs g2pA_taska.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g4pE_taske.txt vs g2pC_taskd.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g4pE_taske.txt vs g4pD_taske.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g4pE_taske.txt vs g4pD_taskd.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g4pE_taske.txt vs g0pB_taska.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g4pE_taske.txt vs g1pB_taske.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g4pE_taske.txt vs g2pA_taskb.txt

g4pE_taske.txt vs g2pA_taskc.txt

g4pE_taske.txt vs g1pD_taska.txt

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g4pE_taske.txt vs g2pB_taska.txt

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g4pE_taske.txt vs g2pE_taskb.txt

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g4pE_taske.txt vs g4pE_taskc.txt

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g4pE_taske.txt vs g0pD_taskd.txt

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g4pE_taske.txt vs g0pE_taskd.txt

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g4pE_taske.txt vs g1pA_taskb.txt

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g4pE_taske.txt vs g1pB_taskb.txt

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g4pE_taske.txt vs g4pE_taskd.txt

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g4pE_taske.txt vs g2pC_taska.txt

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g4pE_taske.txt vs g2pC_taskc.txt

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g4pE_taske.txt vs g2pE_taska.txt

g4pE_taske.txt vs orig_taske.txt

g4pE_taske.txt vs g0pB_taskc.txt

The vector space model has the following limitations:

g4pE_taske.txt vs g0pC_taskd.txt

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g4pE_taske.txt vs g0pC_taske.txt

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g4pE_taske.txt vs g0pD_taskc.txt

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g4pE_taske.txt vs g0pC_taskb.txt

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g4pE_taske.txt vs g2pE_taske.txt

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g4pE_taske.txt vs g0pC_taska.txt

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g4pE_taske.txt vs g0pD_taska.txt

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g4pE_taske.txt vs g4pC_taska.txt

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g4pE_taske.txt vs g1pB_taskc.txt

g4pE_taske.txt vs g1pD_taskc.txt

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g4pE_taske.txt vs g2pB_taske.txt

g4pE_taske.txt vs g2pE_taskc.txt

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g1pD_taskb.txt vs g3pC_taska.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

g1pD_taskb.txt vs g4pD_taskc.txt

g1pD_taskb.txt vs g4pE_taskb.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

g1pD_taskb.txt vs g0pB_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g1pD_taskb.txt vs g1pA_taska.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g1pD_taskb.txt vs g1pA_taske.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g1pD_taskb.txt vs g4pB_taske.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g1pD_taskb.txt vs g2pE_taskd.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g1pD_taskb.txt vs g4pB_taska.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g1pD_taskb.txt vs g4pB_taskd.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g1pD_taskb.txt vs g4pC_taskc.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g1pD_taskb.txt vs g0pE_taskb.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g1pD_taskb.txt vs g1pD_taske.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g1pD_taskb.txt vs g2pB_taskb.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g1pD_taskb.txt vs g2pB_taskd.txt

g1pD_taskb.txt vs g3pA_taske.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g1pD_taskb.txt vs g4pC_taskd.txt

g1pD_taskb.txt vs orig_taskb.txt

g1pD_taskb.txt vs g0pE_taskc.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g1pD_taskb.txt vs g2pB_taskc.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g1pD_taskb.txt vs g2pC_taske.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g1pD_taskb.txt vs g3pA_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g1pD_taskb.txt vs g1pA_taskc.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g1pD_taskb.txt vs g3pA_taskb.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g1pD_taskb.txt vs orig_taska.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g1pD_taskb.txt vs orig_taskd.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g1pD_taskb.txt vs g0pA_taskb.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g1pD_taskb.txt vs g0pB_taske.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g1pD_taskb.txt vs g0pD_taskb.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g1pD_taskb.txt vs g0pD_taske.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g1pD_taskb.txt vs g3pB_taskc.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g1pD_taskb.txt vs g3pC_taskc.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g1pD_taskb.txt vs g4pC_taskb.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g1pD_taskb.txt vs g4pC_taske.txt

g1pD_taskb.txt vs g0pA_taske.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g1pD_taskb.txt vs g0pE_taska.txt

g1pD_taskb.txt vs g3pA_taska.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g1pD_taskb.txt vs g3pB_taska.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g1pD_taskb.txt vs g4pD_taska.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g1pD_taskb.txt vs orig_taskc.txt

g1pD_taskb.txt vs g0pA_taskc.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g1pD_taskb.txt vs g2pA_taska.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g1pD_taskb.txt vs g2pC_taskd.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g1pD_taskb.txt vs g4pD_taske.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g1pD_taskb.txt vs g4pD_taskd.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g1pD_taskb.txt vs g0pB_taska.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g1pD_taskb.txt vs g1pB_taske.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g1pD_taskb.txt vs g2pA_taskb.txt

g1pD_taskb.txt vs g2pA_taskc.txt

g1pD_taskb.txt vs g1pD_taska.txt

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g1pD_taskb.txt vs g2pB_taska.txt

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g1pD_taskb.txt vs g2pE_taskb.txt

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g1pD_taskb.txt vs g4pE_taskc.txt

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g1pD_taskb.txt vs g0pD_taskd.txt

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g1pD_taskb.txt vs g0pE_taskd.txt

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g1pD_taskb.txt vs g1pA_taskb.txt

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g1pD_taskb.txt vs g1pB_taskb.txt

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g1pD_taskb.txt vs g4pE_taskd.txt

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g1pD_taskb.txt vs g2pC_taska.txt

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g1pD_taskb.txt vs g2pC_taskc.txt

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g1pD_taskb.txt vs g2pE_taska.txt

g1pD_taskb.txt vs orig_taske.txt

g1pD_taskb.txt vs g0pB_taskc.txt

The vector space model has the following limitations:

g1pD_taskb.txt vs g0pC_taskd.txt

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g1pD_taskb.txt vs g0pC_taske.txt

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g1pD_taskb.txt vs g0pD_taskc.txt

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g1pD_taskb.txt vs g0pC_taskb.txt

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g1pD_taskb.txt vs g2pE_taske.txt

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g1pD_taskb.txt vs g0pC_taska.txt

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g1pD_taskb.txt vs g0pD_taska.txt

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g1pD_taskb.txt vs g4pC_taska.txt

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g1pD_taskb.txt vs g1pB_taskc.txt

g1pD_taskb.txt vs g1pD_taskc.txt

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g1pD_taskb.txt vs g2pB_taske.txt

g1pD_taskb.txt vs g2pE_taskc.txt

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g3pC_taska.txt vs g4pD_taskc.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

g3pC_taska.txt vs g4pE_taskb.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

g3pC_taska.txt vs g0pB_taskd.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g3pC_taska.txt vs g1pA_taska.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g3pC_taska.txt vs g1pA_taske.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g3pC_taska.txt vs g4pB_taske.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g3pC_taska.txt vs g2pE_taskd.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g3pC_taska.txt vs g4pB_taska.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g3pC_taska.txt vs g4pB_taskd.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g3pC_taska.txt vs g4pC_taskc.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g3pC_taska.txt vs g0pE_taskb.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g3pC_taska.txt vs g1pD_taske.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g3pC_taska.txt vs g2pB_taskb.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g3pC_taska.txt vs g2pB_taskd.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

g3pC_taska.txt vs g3pA_taske.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g3pC_taska.txt vs g4pC_taskd.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

g3pC_taska.txt vs orig_taskb.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

g3pC_taska.txt vs g0pE_taskc.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g3pC_taska.txt vs g2pB_taskc.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g3pC_taska.txt vs g2pC_taske.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g3pC_taska.txt vs g3pA_taskd.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g3pC_taska.txt vs g1pA_taskc.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g3pC_taska.txt vs g3pA_taskb.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g3pC_taska.txt vs orig_taska.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g3pC_taska.txt vs orig_taskd.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g3pC_taska.txt vs g0pA_taskb.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g3pC_taska.txt vs g0pB_taske.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g3pC_taska.txt vs g0pD_taskb.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g3pC_taska.txt vs g0pD_taske.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g3pC_taska.txt vs g3pB_taskc.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g3pC_taska.txt vs g3pC_taskc.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g3pC_taska.txt vs g4pC_taskb.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g3pC_taska.txt vs g4pC_taske.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

g3pC_taska.txt vs g0pA_taske.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g3pC_taska.txt vs g0pE_taska.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

g3pC_taska.txt vs g3pA_taska.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g3pC_taska.txt vs g3pB_taska.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g3pC_taska.txt vs g4pD_taska.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g3pC_taska.txt vs orig_taskc.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

g3pC_taska.txt vs g0pA_taskc.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g3pC_taska.txt vs g2pA_taska.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g3pC_taska.txt vs g2pC_taskd.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g3pC_taska.txt vs g4pD_taske.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g3pC_taska.txt vs g4pD_taskd.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g3pC_taska.txt vs g0pB_taska.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g3pC_taska.txt vs g1pB_taske.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g3pC_taska.txt vs g2pA_taskb.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

g3pC_taska.txt vs g2pA_taskc.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

g3pC_taska.txt vs g1pD_taska.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g3pC_taska.txt vs g2pB_taska.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g3pC_taska.txt vs g2pE_taskb.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g3pC_taska.txt vs g4pE_taskc.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g3pC_taska.txt vs g0pD_taskd.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g3pC_taska.txt vs g0pE_taskd.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g3pC_taska.txt vs g1pA_taskb.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g3pC_taska.txt vs g1pB_taskb.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g3pC_taska.txt vs g4pE_taskd.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g3pC_taska.txt vs g2pC_taska.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g3pC_taska.txt vs g2pC_taskc.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g3pC_taska.txt vs g2pE_taska.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

g3pC_taska.txt vs orig_taske.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

g3pC_taska.txt vs g0pB_taskc.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

The vector space model has the following limitations:

g3pC_taska.txt vs g0pC_taskd.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g3pC_taska.txt vs g0pC_taske.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g3pC_taska.txt vs g0pD_taskc.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g3pC_taska.txt vs g0pC_taskb.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g3pC_taska.txt vs g2pE_taske.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g3pC_taska.txt vs g0pC_taska.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g3pC_taska.txt vs g0pD_taska.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g3pC_taska.txt vs g4pC_taska.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g3pC_taska.txt vs g1pB_taskc.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

g3pC_taska.txt vs g1pD_taskc.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g3pC_taska.txt vs g2pB_taske.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

g3pC_taska.txt vs g2pE_taskc.txt

In object-oriented programming, inheritance is a way to form new classes
(instances of which are called objects) using classes that have already
been defined.

Inheritance is also sometimes called generalization, because the is-a
relationships represent a hierarchy between classes of objects. For
instance, a "fruit" is a generalization of "apple", "orange", "mango"
and many others. One can consider fruit to be an abstraction of apple,
orange, etc. Conversely, since apples are fruit (i.e., an apple is-a
fruit), apples may naturally inherit all the properties common to all
ruit, such as being a fleshy container for the seed of a plant.

Inheritance is typically accomplished either by overriding (replacing)
one or more methods exposed by ancestor, or by adding new methods to
those exposed by an ancestor.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g4pD_taskc.txt vs g4pE_taskb.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

g4pD_taskc.txt vs g0pB_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g4pD_taskc.txt vs g1pA_taska.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g4pD_taskc.txt vs g1pA_taske.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g4pD_taskc.txt vs g4pB_taske.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g4pD_taskc.txt vs g2pE_taskd.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g4pD_taskc.txt vs g4pB_taska.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g4pD_taskc.txt vs g4pB_taskd.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g4pD_taskc.txt vs g4pC_taskc.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g4pD_taskc.txt vs g0pE_taskb.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g4pD_taskc.txt vs g1pD_taske.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g4pD_taskc.txt vs g2pB_taskb.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g4pD_taskc.txt vs g2pB_taskd.txt

g4pD_taskc.txt vs g3pA_taske.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g4pD_taskc.txt vs g4pC_taskd.txt

g4pD_taskc.txt vs orig_taskb.txt

g4pD_taskc.txt vs g0pE_taskc.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g4pD_taskc.txt vs g2pB_taskc.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g4pD_taskc.txt vs g2pC_taske.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g4pD_taskc.txt vs g3pA_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g4pD_taskc.txt vs g1pA_taskc.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g4pD_taskc.txt vs g3pA_taskb.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g4pD_taskc.txt vs orig_taska.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g4pD_taskc.txt vs orig_taskd.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g4pD_taskc.txt vs g0pA_taskb.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g4pD_taskc.txt vs g0pB_taske.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g4pD_taskc.txt vs g0pD_taskb.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g4pD_taskc.txt vs g0pD_taske.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g4pD_taskc.txt vs g3pB_taskc.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g4pD_taskc.txt vs g3pC_taskc.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g4pD_taskc.txt vs g4pC_taskb.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g4pD_taskc.txt vs g4pC_taske.txt

g4pD_taskc.txt vs g0pA_taske.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g4pD_taskc.txt vs g0pE_taska.txt

g4pD_taskc.txt vs g3pA_taska.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g4pD_taskc.txt vs g3pB_taska.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g4pD_taskc.txt vs g4pD_taska.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g4pD_taskc.txt vs orig_taskc.txt

g4pD_taskc.txt vs g0pA_taskc.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g4pD_taskc.txt vs g2pA_taska.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g4pD_taskc.txt vs g2pC_taskd.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g4pD_taskc.txt vs g4pD_taske.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g4pD_taskc.txt vs g4pD_taskd.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g4pD_taskc.txt vs g0pB_taska.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g4pD_taskc.txt vs g1pB_taske.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g4pD_taskc.txt vs g2pA_taskb.txt

g4pD_taskc.txt vs g2pA_taskc.txt

g4pD_taskc.txt vs g1pD_taska.txt

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g4pD_taskc.txt vs g2pB_taska.txt

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g4pD_taskc.txt vs g2pE_taskb.txt

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g4pD_taskc.txt vs g4pE_taskc.txt

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g4pD_taskc.txt vs g0pD_taskd.txt

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g4pD_taskc.txt vs g0pE_taskd.txt

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g4pD_taskc.txt vs g1pA_taskb.txt

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g4pD_taskc.txt vs g1pB_taskb.txt

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g4pD_taskc.txt vs g4pE_taskd.txt

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g4pD_taskc.txt vs g2pC_taska.txt

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g4pD_taskc.txt vs g2pC_taskc.txt

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g4pD_taskc.txt vs g2pE_taska.txt

g4pD_taskc.txt vs orig_taske.txt

g4pD_taskc.txt vs g0pB_taskc.txt

The vector space model has the following limitations:

g4pD_taskc.txt vs g0pC_taskd.txt

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g4pD_taskc.txt vs g0pC_taske.txt

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g4pD_taskc.txt vs g0pD_taskc.txt

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g4pD_taskc.txt vs g0pC_taskb.txt

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g4pD_taskc.txt vs g2pE_taske.txt

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g4pD_taskc.txt vs g0pC_taska.txt

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g4pD_taskc.txt vs g0pD_taska.txt

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g4pD_taskc.txt vs g4pC_taska.txt

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g4pD_taskc.txt vs g1pB_taskc.txt

g4pD_taskc.txt vs g1pD_taskc.txt

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g4pD_taskc.txt vs g2pB_taske.txt

g4pD_taskc.txt vs g2pE_taskc.txt

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g4pE_taskb.txt vs g0pB_taskd.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g4pE_taskb.txt vs g1pA_taska.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g4pE_taskb.txt vs g1pA_taske.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g4pE_taskb.txt vs g4pB_taske.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g4pE_taskb.txt vs g2pE_taskd.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g4pE_taskb.txt vs g4pB_taska.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g4pE_taskb.txt vs g4pB_taskd.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g4pE_taskb.txt vs g4pC_taskc.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g4pE_taskb.txt vs g0pE_taskb.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g4pE_taskb.txt vs g1pD_taske.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g4pE_taskb.txt vs g2pB_taskb.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g4pE_taskb.txt vs g2pB_taskd.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

g4pE_taskb.txt vs g3pA_taske.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g4pE_taskb.txt vs g4pC_taskd.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

g4pE_taskb.txt vs orig_taskb.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

g4pE_taskb.txt vs g0pE_taskc.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g4pE_taskb.txt vs g2pB_taskc.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g4pE_taskb.txt vs g2pC_taske.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g4pE_taskb.txt vs g3pA_taskd.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g4pE_taskb.txt vs g1pA_taskc.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g4pE_taskb.txt vs g3pA_taskb.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g4pE_taskb.txt vs orig_taska.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g4pE_taskb.txt vs orig_taskd.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g4pE_taskb.txt vs g0pA_taskb.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g4pE_taskb.txt vs g0pB_taske.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g4pE_taskb.txt vs g0pD_taskb.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g4pE_taskb.txt vs g0pD_taske.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g4pE_taskb.txt vs g3pB_taskc.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g4pE_taskb.txt vs g3pC_taskc.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g4pE_taskb.txt vs g4pC_taskb.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g4pE_taskb.txt vs g4pC_taske.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

g4pE_taskb.txt vs g0pA_taske.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g4pE_taskb.txt vs g0pE_taska.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

g4pE_taskb.txt vs g3pA_taska.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g4pE_taskb.txt vs g3pB_taska.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g4pE_taskb.txt vs g4pD_taska.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g4pE_taskb.txt vs orig_taskc.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

g4pE_taskb.txt vs g0pA_taskc.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g4pE_taskb.txt vs g2pA_taska.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g4pE_taskb.txt vs g2pC_taskd.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g4pE_taskb.txt vs g4pD_taske.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g4pE_taskb.txt vs g4pD_taskd.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g4pE_taskb.txt vs g0pB_taska.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g4pE_taskb.txt vs g1pB_taske.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g4pE_taskb.txt vs g2pA_taskb.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

g4pE_taskb.txt vs g2pA_taskc.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

g4pE_taskb.txt vs g1pD_taska.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g4pE_taskb.txt vs g2pB_taska.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g4pE_taskb.txt vs g2pE_taskb.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g4pE_taskb.txt vs g4pE_taskc.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g4pE_taskb.txt vs g0pD_taskd.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g4pE_taskb.txt vs g0pE_taskd.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g4pE_taskb.txt vs g1pA_taskb.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g4pE_taskb.txt vs g1pB_taskb.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g4pE_taskb.txt vs g4pE_taskd.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g4pE_taskb.txt vs g2pC_taska.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g4pE_taskb.txt vs g2pC_taskc.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g4pE_taskb.txt vs g2pE_taska.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

g4pE_taskb.txt vs orig_taske.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

g4pE_taskb.txt vs g0pB_taskc.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

The vector space model has the following limitations:

g4pE_taskb.txt vs g0pC_taskd.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g4pE_taskb.txt vs g0pC_taske.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g4pE_taskb.txt vs g0pD_taskc.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g4pE_taskb.txt vs g0pC_taskb.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g4pE_taskb.txt vs g2pE_taske.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g4pE_taskb.txt vs g0pC_taska.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g4pE_taskb.txt vs g0pD_taska.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g4pE_taskb.txt vs g4pC_taska.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g4pE_taskb.txt vs g1pB_taskc.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

g4pE_taskb.txt vs g1pD_taskc.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g4pE_taskb.txt vs g2pB_taske.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

g4pE_taskb.txt vs g2pE_taskc.txt

PageRankalgorithm is also known as link analysis algorithm.  It has been used by google. The algorithm may be applied to any collection of entities with reciprocal quotations and hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring references. The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
The name "PageRank" is a trademark of Google, and the PageRank process has been patented (U.S. Patent 6,285,999 ). However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University. 
In other words, a PageRank results from a "ballot" among all the other pages on the World Wide Web about how important a page is. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ("incoming links"). 
Numerous academic papers concerning PageRank have been published since Page and Brin's original paper.[4] In practice, the PageRank concept has proven to be vulnerable to manipulation, and extensive research has been devoted to identifying falsely inflated PageRank and ways to ignore links from documents with falsely inflated PageRank
	�

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g0pB_taskd.txt vs g1pA_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g0pB_taskd.txt vs g1pA_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g0pB_taskd.txt vs g4pB_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g0pB_taskd.txt vs g2pE_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g0pB_taskd.txt vs g4pB_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g0pB_taskd.txt vs g4pB_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g0pB_taskd.txt vs g4pC_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g0pB_taskd.txt vs g0pE_taskb.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g0pB_taskd.txt vs g1pD_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g0pB_taskd.txt vs g2pB_taskb.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g0pB_taskd.txt vs g2pB_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g0pB_taskd.txt vs g3pA_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g0pB_taskd.txt vs g4pC_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g0pB_taskd.txt vs orig_taskb.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g0pB_taskd.txt vs g0pE_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g0pB_taskd.txt vs g2pB_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g0pB_taskd.txt vs g2pC_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g0pB_taskd.txt vs g3pA_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g0pB_taskd.txt vs g1pA_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g0pB_taskd.txt vs g3pA_taskb.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g0pB_taskd.txt vs orig_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g0pB_taskd.txt vs orig_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g0pB_taskd.txt vs g0pA_taskb.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g0pB_taskd.txt vs g0pB_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g0pB_taskd.txt vs g0pD_taskb.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g0pB_taskd.txt vs g0pD_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g0pB_taskd.txt vs g3pB_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g0pB_taskd.txt vs g3pC_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g0pB_taskd.txt vs g4pC_taskb.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g0pB_taskd.txt vs g4pC_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g0pB_taskd.txt vs g0pA_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g0pB_taskd.txt vs g0pE_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g0pB_taskd.txt vs g3pA_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g0pB_taskd.txt vs g3pB_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g0pB_taskd.txt vs g4pD_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g0pB_taskd.txt vs orig_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g0pB_taskd.txt vs g0pA_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g0pB_taskd.txt vs g2pA_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g0pB_taskd.txt vs g2pC_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g0pB_taskd.txt vs g4pD_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g0pB_taskd.txt vs g4pD_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g0pB_taskd.txt vs g0pB_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g0pB_taskd.txt vs g1pB_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g0pB_taskd.txt vs g2pA_taskb.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g0pB_taskd.txt vs g2pA_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g0pB_taskd.txt vs g1pD_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g0pB_taskd.txt vs g2pB_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g0pB_taskd.txt vs g2pE_taskb.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g0pB_taskd.txt vs g4pE_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g0pB_taskd.txt vs g0pD_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g0pB_taskd.txt vs g0pE_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g0pB_taskd.txt vs g1pA_taskb.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g0pB_taskd.txt vs g1pB_taskb.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g0pB_taskd.txt vs g4pE_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g0pB_taskd.txt vs g2pC_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g0pB_taskd.txt vs g2pC_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g0pB_taskd.txt vs g2pE_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g0pB_taskd.txt vs orig_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g0pB_taskd.txt vs g0pB_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

The vector space model has the following limitations:

g0pB_taskd.txt vs g0pC_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g0pB_taskd.txt vs g0pC_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g0pB_taskd.txt vs g0pD_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g0pB_taskd.txt vs g0pC_taskb.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g0pB_taskd.txt vs g2pE_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g0pB_taskd.txt vs g0pC_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g0pB_taskd.txt vs g0pD_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g0pB_taskd.txt vs g4pC_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g0pB_taskd.txt vs g1pB_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g0pB_taskd.txt vs g1pD_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g0pB_taskd.txt vs g2pB_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

g0pB_taskd.txt vs g2pE_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of
two random events. For example, a person may be seen to have certain
medical symptoms; Bayes' theorem can then be used to compute the
probability that, given that observation, the proposed diagnosis is
the right one.

Bayes' theorem forms a relationship between the probabilities xcof
events A and B. Intuitively, Bayes' theorem in this form describes the
way in which one's recognition of 'A' are updated by having observed
'B'.

P(A | B) = P(B | A) P(A) / P(B)

P(A|B) is the conditional probability of A given B. It is derived from or depends upon the specified value of B, therefore it is also known as the posterior probability.

P(B|A) is the conditional probability of B given A.

P(A) is the prior probability A. It doesn't take into account any information about B, so it is "prior".

P(B) is the prior or marginal probability of B, and acts to normalise the probability.

To derive the theorem, we begin with the definition of conditional
probability. By combining and re-arranging these two equations for A
and B, we get a the lemma called product rule for
probabilities. Provided that P(B) is not a zero, dividing both sides
by P(B) renders us with Bayes' theorem.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g1pA_taska.txt vs g1pA_taske.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g1pA_taska.txt vs g4pB_taske.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g1pA_taska.txt vs g2pE_taskd.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g1pA_taska.txt vs g4pB_taska.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g1pA_taska.txt vs g4pB_taskd.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g1pA_taska.txt vs g4pC_taskc.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g1pA_taska.txt vs g0pE_taskb.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g1pA_taska.txt vs g1pD_taske.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g1pA_taska.txt vs g2pB_taskb.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g1pA_taska.txt vs g2pB_taskd.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g1pA_taska.txt vs g3pA_taske.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g1pA_taska.txt vs g4pC_taskd.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g1pA_taska.txt vs orig_taskb.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g1pA_taska.txt vs g0pE_taskc.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g1pA_taska.txt vs g2pB_taskc.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g1pA_taska.txt vs g2pC_taske.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g1pA_taska.txt vs g3pA_taskd.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g1pA_taska.txt vs g1pA_taskc.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g1pA_taska.txt vs g3pA_taskb.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g1pA_taska.txt vs orig_taska.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g1pA_taska.txt vs orig_taskd.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g1pA_taska.txt vs g0pA_taskb.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g1pA_taska.txt vs g0pB_taske.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g1pA_taska.txt vs g0pD_taskb.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g1pA_taska.txt vs g0pD_taske.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g1pA_taska.txt vs g3pB_taskc.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g1pA_taska.txt vs g3pC_taskc.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g1pA_taska.txt vs g4pC_taskb.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g1pA_taska.txt vs g4pC_taske.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g1pA_taska.txt vs g0pA_taske.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g1pA_taska.txt vs g0pE_taska.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g1pA_taska.txt vs g3pA_taska.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g1pA_taska.txt vs g3pB_taska.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g1pA_taska.txt vs g4pD_taska.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g1pA_taska.txt vs orig_taskc.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g1pA_taska.txt vs g0pA_taskc.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g1pA_taska.txt vs g2pA_taska.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g1pA_taska.txt vs g2pC_taskd.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g1pA_taska.txt vs g4pD_taske.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g1pA_taska.txt vs g4pD_taskd.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g1pA_taska.txt vs g0pB_taska.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g1pA_taska.txt vs g1pB_taske.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g1pA_taska.txt vs g2pA_taskb.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g1pA_taska.txt vs g2pA_taskc.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g1pA_taska.txt vs g1pD_taska.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g1pA_taska.txt vs g2pB_taska.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g1pA_taska.txt vs g2pE_taskb.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g1pA_taska.txt vs g4pE_taskc.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g1pA_taska.txt vs g0pD_taskd.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g1pA_taska.txt vs g0pE_taskd.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g1pA_taska.txt vs g1pA_taskb.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g1pA_taska.txt vs g1pB_taskb.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g1pA_taska.txt vs g4pE_taskd.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g1pA_taska.txt vs g2pC_taska.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g1pA_taska.txt vs g2pC_taskc.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g1pA_taska.txt vs g2pE_taska.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g1pA_taska.txt vs orig_taske.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g1pA_taska.txt vs g0pB_taskc.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

The vector space model has the following limitations:

g1pA_taska.txt vs g0pC_taskd.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g1pA_taska.txt vs g0pC_taske.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g1pA_taska.txt vs g0pD_taskc.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g1pA_taska.txt vs g0pC_taskb.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g1pA_taska.txt vs g2pE_taske.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g1pA_taska.txt vs g0pC_taska.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g1pA_taska.txt vs g0pD_taska.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g1pA_taska.txt vs g4pC_taska.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g1pA_taska.txt vs g1pB_taskc.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g1pA_taska.txt vs g1pD_taskc.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g1pA_taska.txt vs g2pB_taske.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

g1pA_taska.txt vs g2pE_taskc.txt

In object oriented programming, objects are grouped together into classes according to their type, structure and the functions that can be performed on them. Inheritance is a process in object oriented programming in which objects acquire (or inherit) the properties of objects of another class. It is therefore used to create relationships between one object and another. Each class groups together objects of a similar type, with similar properties. New classes can be formed by this process whose objects will have properties of both the classes from which this new class is formed. A superclass has all of the properties of the subclasses below it. At the same time subclasses are each distinctive from each other but related via the superclass. Subclasses are said to ‘extend’ superclasses. Due to these relationships, object oriented programmes tend to be easier to modify since they do not need to be changed when a new object, with different properties is added. Instead, a new object is made to inherit properties of objects which already exist. Inheritance can be divided into two main processes: single inheritance and multiple inheritance. Single inheritance means that the class can only inherit from one other class, whereas multiple inheritance allows for inheritance from several classes.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g1pA_taske.txt vs g4pB_taske.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g1pA_taske.txt vs g2pE_taskd.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g1pA_taske.txt vs g4pB_taska.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g1pA_taske.txt vs g4pB_taskd.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g1pA_taske.txt vs g4pC_taskc.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g1pA_taske.txt vs g0pE_taskb.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g1pA_taske.txt vs g1pD_taske.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g1pA_taske.txt vs g2pB_taskb.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g1pA_taske.txt vs g2pB_taskd.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g1pA_taske.txt vs g3pA_taske.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g1pA_taske.txt vs g4pC_taskd.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g1pA_taske.txt vs orig_taskb.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g1pA_taske.txt vs g0pE_taskc.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g1pA_taske.txt vs g2pB_taskc.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g1pA_taske.txt vs g2pC_taske.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g1pA_taske.txt vs g3pA_taskd.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g1pA_taske.txt vs g1pA_taskc.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g1pA_taske.txt vs g3pA_taskb.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g1pA_taske.txt vs orig_taska.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g1pA_taske.txt vs orig_taskd.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g1pA_taske.txt vs g0pA_taskb.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g1pA_taske.txt vs g0pB_taske.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g1pA_taske.txt vs g0pD_taskb.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g1pA_taske.txt vs g0pD_taske.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g1pA_taske.txt vs g3pB_taskc.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g1pA_taske.txt vs g3pC_taskc.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g1pA_taske.txt vs g4pC_taskb.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g1pA_taske.txt vs g4pC_taske.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g1pA_taske.txt vs g0pA_taske.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g1pA_taske.txt vs g0pE_taska.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g1pA_taske.txt vs g3pA_taska.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g1pA_taske.txt vs g3pB_taska.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g1pA_taske.txt vs g4pD_taska.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g1pA_taske.txt vs orig_taskc.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g1pA_taske.txt vs g0pA_taskc.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g1pA_taske.txt vs g2pA_taska.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g1pA_taske.txt vs g2pC_taskd.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g1pA_taske.txt vs g4pD_taske.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g1pA_taske.txt vs g4pD_taskd.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g1pA_taske.txt vs g0pB_taska.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g1pA_taske.txt vs g1pB_taske.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g1pA_taske.txt vs g2pA_taskb.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g1pA_taske.txt vs g2pA_taskc.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g1pA_taske.txt vs g1pD_taska.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g1pA_taske.txt vs g2pB_taska.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g1pA_taske.txt vs g2pE_taskb.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g1pA_taske.txt vs g4pE_taskc.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g1pA_taske.txt vs g0pD_taskd.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g1pA_taske.txt vs g0pE_taskd.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g1pA_taske.txt vs g1pA_taskb.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g1pA_taske.txt vs g1pB_taskb.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g1pA_taske.txt vs g4pE_taskd.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g1pA_taske.txt vs g2pC_taska.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g1pA_taske.txt vs g2pC_taskc.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g1pA_taske.txt vs g2pE_taska.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g1pA_taske.txt vs orig_taske.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g1pA_taske.txt vs g0pB_taskc.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

The vector space model has the following limitations:

g1pA_taske.txt vs g0pC_taskd.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g1pA_taske.txt vs g0pC_taske.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g1pA_taske.txt vs g0pD_taskc.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g1pA_taske.txt vs g0pC_taskb.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g1pA_taske.txt vs g2pE_taske.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g1pA_taske.txt vs g0pC_taska.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g1pA_taske.txt vs g0pD_taska.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g1pA_taske.txt vs g4pC_taska.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g1pA_taske.txt vs g1pB_taskc.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g1pA_taske.txt vs g1pD_taskc.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g1pA_taske.txt vs g2pB_taske.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

g1pA_taske.txt vs g2pE_taskc.txt

Dynamic programming is an algorithmic technique used to solve certain optimization problems where the object is to find the best solution from a number of possibilities. It uses a so called ‘bottom-up’ approach, meaning that the problem is solved as a set of sub-problems which in turn are made up of sub-sub-problems.Sub-problems are then selected and used to solve the overall problem. These sub-problems are only solved once and the solutions are saved so that they will not need to be recalculated again. Whilst calculated individually, they may also overlap. When any sub-problem is met again, it can be found and re-used to solve another problem. Since it searches all possibilities, it is also very accurate. This method is far more efficient than recalculating and therefore considerably reduces computation. It is widely used in computer science and can be applied for example, to compress data in high density bar codes.

Dynamic programming is most effective and therefore most often used on objects that are ordered from left to right and whose order cannot be rearranged. This means it works well on character chains for example.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g4pB_taske.txt vs g2pE_taskd.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g4pB_taske.txt vs g4pB_taska.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g4pB_taske.txt vs g4pB_taskd.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g4pB_taske.txt vs g4pC_taskc.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g4pB_taske.txt vs g0pE_taskb.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g4pB_taske.txt vs g1pD_taske.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g4pB_taske.txt vs g2pB_taskb.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g4pB_taske.txt vs g2pB_taskd.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g4pB_taske.txt vs g3pA_taske.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g4pB_taske.txt vs g4pC_taskd.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g4pB_taske.txt vs orig_taskb.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g4pB_taske.txt vs g0pE_taskc.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g4pB_taske.txt vs g2pB_taskc.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g4pB_taske.txt vs g2pC_taske.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g4pB_taske.txt vs g3pA_taskd.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g4pB_taske.txt vs g1pA_taskc.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g4pB_taske.txt vs g3pA_taskb.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g4pB_taske.txt vs orig_taska.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g4pB_taske.txt vs orig_taskd.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g4pB_taske.txt vs g0pA_taskb.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g4pB_taske.txt vs g0pB_taske.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g4pB_taske.txt vs g0pD_taskb.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g4pB_taske.txt vs g0pD_taske.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g4pB_taske.txt vs g3pB_taskc.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g4pB_taske.txt vs g3pC_taskc.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g4pB_taske.txt vs g4pC_taskb.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g4pB_taske.txt vs g4pC_taske.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g4pB_taske.txt vs g0pA_taske.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g4pB_taske.txt vs g0pE_taska.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g4pB_taske.txt vs g3pA_taska.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g4pB_taske.txt vs g3pB_taska.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g4pB_taske.txt vs g4pD_taska.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g4pB_taske.txt vs orig_taskc.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g4pB_taske.txt vs g0pA_taskc.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g4pB_taske.txt vs g2pA_taska.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g4pB_taske.txt vs g2pC_taskd.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g4pB_taske.txt vs g4pD_taske.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g4pB_taske.txt vs g4pD_taskd.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g4pB_taske.txt vs g0pB_taska.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g4pB_taske.txt vs g1pB_taske.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g4pB_taske.txt vs g2pA_taskb.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g4pB_taske.txt vs g2pA_taskc.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g4pB_taske.txt vs g1pD_taska.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g4pB_taske.txt vs g2pB_taska.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g4pB_taske.txt vs g2pE_taskb.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g4pB_taske.txt vs g4pE_taskc.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g4pB_taske.txt vs g0pD_taskd.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g4pB_taske.txt vs g0pE_taskd.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g4pB_taske.txt vs g1pA_taskb.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g4pB_taske.txt vs g1pB_taskb.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g4pB_taske.txt vs g4pE_taskd.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g4pB_taske.txt vs g2pC_taska.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g4pB_taske.txt vs g2pC_taskc.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g4pB_taske.txt vs g2pE_taska.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g4pB_taske.txt vs orig_taske.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g4pB_taske.txt vs g0pB_taskc.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

The vector space model has the following limitations:

g4pB_taske.txt vs g0pC_taskd.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g4pB_taske.txt vs g0pC_taske.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g4pB_taske.txt vs g0pD_taskc.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g4pB_taske.txt vs g0pC_taskb.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g4pB_taske.txt vs g2pE_taske.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g4pB_taske.txt vs g0pC_taska.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g4pB_taske.txt vs g0pD_taska.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g4pB_taske.txt vs g4pC_taska.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g4pB_taske.txt vs g1pB_taskc.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g4pB_taske.txt vs g1pD_taskc.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g4pB_taske.txt vs g2pB_taske.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

g4pB_taske.txt vs g2pE_taskc.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping subproblems and optimal substructure.

The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.

dynamic programming makes use of:

Overlapping subproblems
Optimal substructure
Memoization

Dynamic programming usually takes one of two approaches:

Top-down approach
Bottom-up approach

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g2pE_taskd.txt vs g4pB_taska.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g2pE_taskd.txt vs g4pB_taskd.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g2pE_taskd.txt vs g4pC_taskc.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g2pE_taskd.txt vs g0pE_taskb.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g2pE_taskd.txt vs g1pD_taske.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g2pE_taskd.txt vs g2pB_taskb.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g2pE_taskd.txt vs g2pB_taskd.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g2pE_taskd.txt vs g3pA_taske.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g2pE_taskd.txt vs g4pC_taskd.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g2pE_taskd.txt vs orig_taskb.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g2pE_taskd.txt vs g0pE_taskc.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g2pE_taskd.txt vs g2pB_taskc.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g2pE_taskd.txt vs g2pC_taske.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g2pE_taskd.txt vs g3pA_taskd.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g2pE_taskd.txt vs g1pA_taskc.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g2pE_taskd.txt vs g3pA_taskb.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g2pE_taskd.txt vs orig_taska.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g2pE_taskd.txt vs orig_taskd.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g2pE_taskd.txt vs g0pA_taskb.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g2pE_taskd.txt vs g0pB_taske.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g2pE_taskd.txt vs g0pD_taskb.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g2pE_taskd.txt vs g0pD_taske.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g2pE_taskd.txt vs g3pB_taskc.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g2pE_taskd.txt vs g3pC_taskc.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g2pE_taskd.txt vs g4pC_taskb.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g2pE_taskd.txt vs g4pC_taske.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g2pE_taskd.txt vs g0pA_taske.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g2pE_taskd.txt vs g0pE_taska.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g2pE_taskd.txt vs g3pA_taska.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g2pE_taskd.txt vs g3pB_taska.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g2pE_taskd.txt vs g4pD_taska.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g2pE_taskd.txt vs orig_taskc.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g2pE_taskd.txt vs g0pA_taskc.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g2pE_taskd.txt vs g2pA_taska.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g2pE_taskd.txt vs g2pC_taskd.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g2pE_taskd.txt vs g4pD_taske.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g2pE_taskd.txt vs g4pD_taskd.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g2pE_taskd.txt vs g0pB_taska.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g2pE_taskd.txt vs g1pB_taske.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g2pE_taskd.txt vs g2pA_taskb.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g2pE_taskd.txt vs g2pA_taskc.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g2pE_taskd.txt vs g1pD_taska.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g2pE_taskd.txt vs g2pB_taska.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g2pE_taskd.txt vs g2pE_taskb.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g2pE_taskd.txt vs g4pE_taskc.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g2pE_taskd.txt vs g0pD_taskd.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g2pE_taskd.txt vs g0pE_taskd.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g2pE_taskd.txt vs g1pA_taskb.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g2pE_taskd.txt vs g1pB_taskb.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g2pE_taskd.txt vs g4pE_taskd.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g2pE_taskd.txt vs g2pC_taska.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g2pE_taskd.txt vs g2pC_taskc.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g2pE_taskd.txt vs g2pE_taska.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g2pE_taskd.txt vs orig_taske.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g2pE_taskd.txt vs g0pB_taskc.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

The vector space model has the following limitations:

g2pE_taskd.txt vs g0pC_taskd.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g2pE_taskd.txt vs g0pC_taske.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g2pE_taskd.txt vs g0pD_taskc.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g2pE_taskd.txt vs g0pC_taskb.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g2pE_taskd.txt vs g2pE_taske.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g2pE_taskd.txt vs g0pC_taska.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g2pE_taskd.txt vs g0pD_taska.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g2pE_taskd.txt vs g4pC_taska.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g2pE_taskd.txt vs g1pB_taskc.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g2pE_taskd.txt vs g1pD_taskc.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g2pE_taskd.txt vs g2pB_taske.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

g2pE_taskd.txt vs g2pE_taskc.txt

The Probability of an event happening mean considering the likelihood of or the number of the instance occurring, and dividing this value by the total number of events. The equation for this calculation would look as follows:
Probability (P) = number of instance / total number of events
On the other hand Probability Theory (P) usually involves assigning values to events. For example:
(P)=1: event is certain to occur
(P)=0: event is certain NOT to occur
(P)=0.5: event occurs half of the time. 

There is also Conditional Probability which is usually interested in the way variables relate to each other. Bayes Theorem is the name given to an important theorem relating
Conditional probabilities and it can be seen as a way of understanding how the probability that a theory is true, is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g4pB_taska.txt vs g4pB_taskd.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g4pB_taska.txt vs g4pC_taskc.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g4pB_taska.txt vs g0pE_taskb.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g4pB_taska.txt vs g1pD_taske.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g4pB_taska.txt vs g2pB_taskb.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g4pB_taska.txt vs g2pB_taskd.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g4pB_taska.txt vs g3pA_taske.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g4pB_taska.txt vs g4pC_taskd.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g4pB_taska.txt vs orig_taskb.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g4pB_taska.txt vs g0pE_taskc.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g4pB_taska.txt vs g2pB_taskc.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g4pB_taska.txt vs g2pC_taske.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g4pB_taska.txt vs g3pA_taskd.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g4pB_taska.txt vs g1pA_taskc.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g4pB_taska.txt vs g3pA_taskb.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g4pB_taska.txt vs orig_taska.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g4pB_taska.txt vs orig_taskd.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g4pB_taska.txt vs g0pA_taskb.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g4pB_taska.txt vs g0pB_taske.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g4pB_taska.txt vs g0pD_taskb.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g4pB_taska.txt vs g0pD_taske.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g4pB_taska.txt vs g3pB_taskc.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g4pB_taska.txt vs g3pC_taskc.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g4pB_taska.txt vs g4pC_taskb.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g4pB_taska.txt vs g4pC_taske.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g4pB_taska.txt vs g0pA_taske.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g4pB_taska.txt vs g0pE_taska.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g4pB_taska.txt vs g3pA_taska.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g4pB_taska.txt vs g3pB_taska.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g4pB_taska.txt vs g4pD_taska.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g4pB_taska.txt vs orig_taskc.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g4pB_taska.txt vs g0pA_taskc.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g4pB_taska.txt vs g2pA_taska.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g4pB_taska.txt vs g2pC_taskd.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g4pB_taska.txt vs g4pD_taske.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g4pB_taska.txt vs g4pD_taskd.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g4pB_taska.txt vs g0pB_taska.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g4pB_taska.txt vs g1pB_taske.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g4pB_taska.txt vs g2pA_taskb.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g4pB_taska.txt vs g2pA_taskc.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g4pB_taska.txt vs g1pD_taska.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g4pB_taska.txt vs g2pB_taska.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g4pB_taska.txt vs g2pE_taskb.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g4pB_taska.txt vs g4pE_taskc.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g4pB_taska.txt vs g0pD_taskd.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g4pB_taska.txt vs g0pE_taskd.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g4pB_taska.txt vs g1pA_taskb.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g4pB_taska.txt vs g1pB_taskb.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g4pB_taska.txt vs g4pE_taskd.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g4pB_taska.txt vs g2pC_taska.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g4pB_taska.txt vs g2pC_taskc.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g4pB_taska.txt vs g2pE_taska.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g4pB_taska.txt vs orig_taske.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g4pB_taska.txt vs g0pB_taskc.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

The vector space model has the following limitations:

g4pB_taska.txt vs g0pC_taskd.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g4pB_taska.txt vs g0pC_taske.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g4pB_taska.txt vs g0pD_taskc.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g4pB_taska.txt vs g0pC_taskb.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g4pB_taska.txt vs g2pE_taske.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g4pB_taska.txt vs g0pC_taska.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g4pB_taska.txt vs g0pD_taska.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g4pB_taska.txt vs g4pC_taska.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g4pB_taska.txt vs g1pB_taskc.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g4pB_taska.txt vs g1pD_taskc.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g4pB_taska.txt vs g2pB_taske.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

g4pB_taska.txt vs g2pE_taskc.txt

Inheritance is the ability of a subclass to inherit default, protected and public attributes and methods from its superclasses. Each object (except java.lang.Object) can be cast to an object of one of its superclasses. However an object cannot be cast to a class which is no relative of it. Here is an example of inheritance:
We have the class of all living things which have attributes like weight and age. We have the classes of animals, plants, viruses and fungi that are subclasses of the class of all living things. The animals have their unique attributes (organs, hair, etc.) and methods (walking, mating, etc.). They also inherit the attributes and methods of its superclass. Animals can be treated (cast) to living things. However, animals cannot be treated as fungi.
In object oriented programming inheritance is also dependant on access level modifiers. For example private attributes and methods cannot be inherited. Virtual attributes and methods can be shadowed/overridden. In Java all attributes and methods are implicitly virtual. Object variable can store a reference to the same class or a subclass (i.e. this or more specialised version). However, object variables cannot store references to a superclass (i.e. less specialised version) of the original class.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g4pB_taskd.txt vs g4pC_taskc.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g4pB_taskd.txt vs g0pE_taskb.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g4pB_taskd.txt vs g1pD_taske.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g4pB_taskd.txt vs g2pB_taskb.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g4pB_taskd.txt vs g2pB_taskd.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g4pB_taskd.txt vs g3pA_taske.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g4pB_taskd.txt vs g4pC_taskd.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g4pB_taskd.txt vs orig_taskb.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g4pB_taskd.txt vs g0pE_taskc.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g4pB_taskd.txt vs g2pB_taskc.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g4pB_taskd.txt vs g2pC_taske.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g4pB_taskd.txt vs g3pA_taskd.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g4pB_taskd.txt vs g1pA_taskc.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g4pB_taskd.txt vs g3pA_taskb.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g4pB_taskd.txt vs orig_taska.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g4pB_taskd.txt vs orig_taskd.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g4pB_taskd.txt vs g0pA_taskb.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g4pB_taskd.txt vs g0pB_taske.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g4pB_taskd.txt vs g0pD_taskb.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g4pB_taskd.txt vs g0pD_taske.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g4pB_taskd.txt vs g3pB_taskc.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g4pB_taskd.txt vs g3pC_taskc.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g4pB_taskd.txt vs g4pC_taskb.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g4pB_taskd.txt vs g4pC_taske.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g4pB_taskd.txt vs g0pA_taske.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g4pB_taskd.txt vs g0pE_taska.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g4pB_taskd.txt vs g3pA_taska.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g4pB_taskd.txt vs g3pB_taska.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g4pB_taskd.txt vs g4pD_taska.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g4pB_taskd.txt vs orig_taskc.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g4pB_taskd.txt vs g0pA_taskc.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g4pB_taskd.txt vs g2pA_taska.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g4pB_taskd.txt vs g2pC_taskd.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g4pB_taskd.txt vs g4pD_taske.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g4pB_taskd.txt vs g4pD_taskd.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g4pB_taskd.txt vs g0pB_taska.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g4pB_taskd.txt vs g1pB_taske.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g4pB_taskd.txt vs g2pA_taskb.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g4pB_taskd.txt vs g2pA_taskc.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g4pB_taskd.txt vs g1pD_taska.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g4pB_taskd.txt vs g2pB_taska.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g4pB_taskd.txt vs g2pE_taskb.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g4pB_taskd.txt vs g4pE_taskc.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g4pB_taskd.txt vs g0pD_taskd.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g4pB_taskd.txt vs g0pE_taskd.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g4pB_taskd.txt vs g1pA_taskb.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g4pB_taskd.txt vs g1pB_taskb.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g4pB_taskd.txt vs g4pE_taskd.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g4pB_taskd.txt vs g2pC_taska.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g4pB_taskd.txt vs g2pC_taskc.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g4pB_taskd.txt vs g2pE_taska.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g4pB_taskd.txt vs orig_taske.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g4pB_taskd.txt vs g0pB_taskc.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

The vector space model has the following limitations:

g4pB_taskd.txt vs g0pC_taskd.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g4pB_taskd.txt vs g0pC_taske.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g4pB_taskd.txt vs g0pD_taskc.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g4pB_taskd.txt vs g0pC_taskb.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g4pB_taskd.txt vs g2pE_taske.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g4pB_taskd.txt vs g0pC_taska.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g4pB_taskd.txt vs g0pD_taska.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g4pB_taskd.txt vs g4pC_taska.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g4pB_taskd.txt vs g1pB_taskc.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g4pB_taskd.txt vs g1pD_taskc.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g4pB_taskd.txt vs g2pB_taske.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

g4pB_taskd.txt vs g2pE_taskc.txt

In probability theory, Bayes' theorem (or Bayes' law after Rev Thomas Bayes) provides relation between the conditional and marginal probabilities of two random events. It is usually used to calculate posterior probabilities given observations. For example: a patient might be observed to show certain symptoms. Bayes' theorem could be used to compute the probability that a certain diagnosis is right, given that observation.

Since it is a formal theorem, Bayes' theorem holds in all popular interpretations of probability. 
Bayes' theorem relates the conditional and marginal probabilities of events a and b, where b has a non-vanishing probability:

    P(a|b) = P(a|b)P(a)/P(b)

Terms in Bayes' theorem are named by a convention:

P(A) is the prior probability or marginal probability of A. It does not take into account any information about B and therefore is considered �prior�.
P(A|B) is the conditional probability of A, given B. It it is derived from or depends upon the specified value of B. Usually it is called the posterior probability 
P(B|A) is the conditional probability of B given A.
P(B) (a.k.a. the normalizing constant) is the prior or marginal probability of B.

Obviously, Bayes' theorem describes the way in which one's assumptions about observing the event'a' are changed by having observed the event 'b'.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g4pC_taskc.txt vs g0pE_taskb.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g4pC_taskc.txt vs g1pD_taske.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g4pC_taskc.txt vs g2pB_taskb.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g4pC_taskc.txt vs g2pB_taskd.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g4pC_taskc.txt vs g3pA_taske.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g4pC_taskc.txt vs g4pC_taskd.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g4pC_taskc.txt vs orig_taskb.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g4pC_taskc.txt vs g0pE_taskc.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g4pC_taskc.txt vs g2pB_taskc.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g4pC_taskc.txt vs g2pC_taske.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g4pC_taskc.txt vs g3pA_taskd.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g4pC_taskc.txt vs g1pA_taskc.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g4pC_taskc.txt vs g3pA_taskb.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g4pC_taskc.txt vs orig_taska.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g4pC_taskc.txt vs orig_taskd.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g4pC_taskc.txt vs g0pA_taskb.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g4pC_taskc.txt vs g0pB_taske.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g4pC_taskc.txt vs g0pD_taskb.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g4pC_taskc.txt vs g0pD_taske.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g4pC_taskc.txt vs g3pB_taskc.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g4pC_taskc.txt vs g3pC_taskc.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g4pC_taskc.txt vs g4pC_taskb.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g4pC_taskc.txt vs g4pC_taske.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g4pC_taskc.txt vs g0pA_taske.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g4pC_taskc.txt vs g0pE_taska.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g4pC_taskc.txt vs g3pA_taska.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g4pC_taskc.txt vs g3pB_taska.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g4pC_taskc.txt vs g4pD_taska.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g4pC_taskc.txt vs orig_taskc.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g4pC_taskc.txt vs g0pA_taskc.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g4pC_taskc.txt vs g2pA_taska.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g4pC_taskc.txt vs g2pC_taskd.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g4pC_taskc.txt vs g4pD_taske.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g4pC_taskc.txt vs g4pD_taskd.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g4pC_taskc.txt vs g0pB_taska.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g4pC_taskc.txt vs g1pB_taske.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g4pC_taskc.txt vs g2pA_taskb.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g4pC_taskc.txt vs g2pA_taskc.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g4pC_taskc.txt vs g1pD_taska.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g4pC_taskc.txt vs g2pB_taska.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g4pC_taskc.txt vs g2pE_taskb.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g4pC_taskc.txt vs g4pE_taskc.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g4pC_taskc.txt vs g0pD_taskd.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g4pC_taskc.txt vs g0pE_taskd.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g4pC_taskc.txt vs g1pA_taskb.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g4pC_taskc.txt vs g1pB_taskb.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g4pC_taskc.txt vs g4pE_taskd.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g4pC_taskc.txt vs g2pC_taska.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g4pC_taskc.txt vs g2pC_taskc.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g4pC_taskc.txt vs g2pE_taska.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g4pC_taskc.txt vs orig_taske.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g4pC_taskc.txt vs g0pB_taskc.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

The vector space model has the following limitations:

g4pC_taskc.txt vs g0pC_taskd.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g4pC_taskc.txt vs g0pC_taske.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g4pC_taskc.txt vs g0pD_taskc.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g4pC_taskc.txt vs g0pC_taskb.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g4pC_taskc.txt vs g2pE_taske.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g4pC_taskc.txt vs g0pC_taska.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g4pC_taskc.txt vs g0pD_taska.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g4pC_taskc.txt vs g4pC_taska.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g4pC_taskc.txt vs g1pB_taskc.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g4pC_taskc.txt vs g1pD_taskc.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g4pC_taskc.txt vs g2pB_taske.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

g4pC_taskc.txt vs g2pE_taskc.txt

The vector space model are the documents which are represented as “bags of words”.The basic idea is to represent each document as a vector of certain weighted word frequencies. In order to do so, the following parsing and extraction steps are needed. 
1.	Ignoring case, extract all unique words from the entire set of documents. 
2.	Eliminate non-content-bearing ``stopwords'' such as ``a'', ``and'', ``the'', etc. For sample lists of stopwords.
3.	For each document, count the number of occurrences of each word. 
4.	Using heuristic or information-theoretic criteria, eliminate non-content-bearing ``high-frequency'' and ``low-frequency'' words. 
5.	After the above elimination, suppose unique words remain. Assign a unique identifier between  and to each remaining word, and a unique identifier between and to each document.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g0pE_taskb.txt vs g1pD_taske.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g0pE_taskb.txt vs g2pB_taskb.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g0pE_taskb.txt vs g2pB_taskd.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g0pE_taskb.txt vs g3pA_taske.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g0pE_taskb.txt vs g4pC_taskd.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g0pE_taskb.txt vs orig_taskb.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g0pE_taskb.txt vs g0pE_taskc.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g0pE_taskb.txt vs g2pB_taskc.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g0pE_taskb.txt vs g2pC_taske.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g0pE_taskb.txt vs g3pA_taskd.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g0pE_taskb.txt vs g1pA_taskc.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g0pE_taskb.txt vs g3pA_taskb.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g0pE_taskb.txt vs orig_taska.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g0pE_taskb.txt vs orig_taskd.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g0pE_taskb.txt vs g0pA_taskb.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g0pE_taskb.txt vs g0pB_taske.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g0pE_taskb.txt vs g0pD_taskb.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g0pE_taskb.txt vs g0pD_taske.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g0pE_taskb.txt vs g3pB_taskc.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g0pE_taskb.txt vs g3pC_taskc.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g0pE_taskb.txt vs g4pC_taskb.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g0pE_taskb.txt vs g4pC_taske.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g0pE_taskb.txt vs g0pA_taske.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g0pE_taskb.txt vs g0pE_taska.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g0pE_taskb.txt vs g3pA_taska.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g0pE_taskb.txt vs g3pB_taska.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g0pE_taskb.txt vs g4pD_taska.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g0pE_taskb.txt vs orig_taskc.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g0pE_taskb.txt vs g0pA_taskc.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g0pE_taskb.txt vs g2pA_taska.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g0pE_taskb.txt vs g2pC_taskd.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g0pE_taskb.txt vs g4pD_taske.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g0pE_taskb.txt vs g4pD_taskd.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g0pE_taskb.txt vs g0pB_taska.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g0pE_taskb.txt vs g1pB_taske.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g0pE_taskb.txt vs g2pA_taskb.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g0pE_taskb.txt vs g2pA_taskc.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g0pE_taskb.txt vs g1pD_taska.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g0pE_taskb.txt vs g2pB_taska.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g0pE_taskb.txt vs g2pE_taskb.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g0pE_taskb.txt vs g4pE_taskc.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g0pE_taskb.txt vs g0pD_taskd.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g0pE_taskb.txt vs g0pE_taskd.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g0pE_taskb.txt vs g1pA_taskb.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g0pE_taskb.txt vs g1pB_taskb.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g0pE_taskb.txt vs g4pE_taskd.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g0pE_taskb.txt vs g2pC_taska.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g0pE_taskb.txt vs g2pC_taskc.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g0pE_taskb.txt vs g2pE_taska.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g0pE_taskb.txt vs orig_taske.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g0pE_taskb.txt vs g0pB_taskc.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

The vector space model has the following limitations:

g0pE_taskb.txt vs g0pC_taskd.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g0pE_taskb.txt vs g0pC_taske.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g0pE_taskb.txt vs g0pD_taskc.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g0pE_taskb.txt vs g0pC_taskb.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g0pE_taskb.txt vs g2pE_taske.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g0pE_taskb.txt vs g0pC_taska.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g0pE_taskb.txt vs g0pD_taska.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g0pE_taskb.txt vs g4pC_taska.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g0pE_taskb.txt vs g1pB_taskc.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g0pE_taskb.txt vs g1pD_taskc.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g0pE_taskb.txt vs g2pB_taske.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

g0pE_taskb.txt vs g2pE_taskc.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. PageRank Uses in google toolbar: Measures popularity of a site ,Marketing value,Updated periodically, in google directory: PageRank: sort links within categories;Volunteers evaluate, classify, annotate;Open Directory project using PageRank.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g1pD_taske.txt vs g2pB_taskb.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g1pD_taske.txt vs g2pB_taskd.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g1pD_taske.txt vs g3pA_taske.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g1pD_taske.txt vs g4pC_taskd.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g1pD_taske.txt vs orig_taskb.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g1pD_taske.txt vs g0pE_taskc.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g1pD_taske.txt vs g2pB_taskc.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g1pD_taske.txt vs g2pC_taske.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g1pD_taske.txt vs g3pA_taskd.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g1pD_taske.txt vs g1pA_taskc.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g1pD_taske.txt vs g3pA_taskb.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g1pD_taske.txt vs orig_taska.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g1pD_taske.txt vs orig_taskd.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g1pD_taske.txt vs g0pA_taskb.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g1pD_taske.txt vs g0pB_taske.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g1pD_taske.txt vs g0pD_taskb.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g1pD_taske.txt vs g0pD_taske.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g1pD_taske.txt vs g3pB_taskc.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g1pD_taske.txt vs g3pC_taskc.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g1pD_taske.txt vs g4pC_taskb.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g1pD_taske.txt vs g4pC_taske.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g1pD_taske.txt vs g0pA_taske.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g1pD_taske.txt vs g0pE_taska.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g1pD_taske.txt vs g3pA_taska.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g1pD_taske.txt vs g3pB_taska.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g1pD_taske.txt vs g4pD_taska.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g1pD_taske.txt vs orig_taskc.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g1pD_taske.txt vs g0pA_taskc.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g1pD_taske.txt vs g2pA_taska.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g1pD_taske.txt vs g2pC_taskd.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g1pD_taske.txt vs g4pD_taske.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g1pD_taske.txt vs g4pD_taskd.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g1pD_taske.txt vs g0pB_taska.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g1pD_taske.txt vs g1pB_taske.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g1pD_taske.txt vs g2pA_taskb.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g1pD_taske.txt vs g2pA_taskc.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g1pD_taske.txt vs g1pD_taska.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g1pD_taske.txt vs g2pB_taska.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g1pD_taske.txt vs g2pE_taskb.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g1pD_taske.txt vs g4pE_taskc.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g1pD_taske.txt vs g0pD_taskd.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g1pD_taske.txt vs g0pE_taskd.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g1pD_taske.txt vs g1pA_taskb.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g1pD_taske.txt vs g1pB_taskb.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g1pD_taske.txt vs g4pE_taskd.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g1pD_taske.txt vs g2pC_taska.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g1pD_taske.txt vs g2pC_taskc.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g1pD_taske.txt vs g2pE_taska.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g1pD_taske.txt vs orig_taske.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g1pD_taske.txt vs g0pB_taskc.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

The vector space model has the following limitations:

g1pD_taske.txt vs g0pC_taskd.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g1pD_taske.txt vs g0pC_taske.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g1pD_taske.txt vs g0pD_taskc.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g1pD_taske.txt vs g0pC_taskb.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g1pD_taske.txt vs g2pE_taske.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g1pD_taske.txt vs g0pC_taska.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g1pD_taske.txt vs g0pD_taska.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g1pD_taske.txt vs g4pC_taska.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g1pD_taske.txt vs g1pB_taskc.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g1pD_taske.txt vs g1pD_taskc.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g1pD_taske.txt vs g2pB_taske.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

g1pD_taske.txt vs g2pE_taskc.txt

Dynamic programming is a faster method of solving problems that make use of optimal substructure, overlapping sub-problems and memoization. It has no relationship to computer programming; instead it is a process of finding a satisfactory algorithm. 

Optimal substructure is the process of using the optional solutions to sub problems to find the optimal solution to the overall problem. When the same sub problem solutions can be used to solve various bigger problems it is said to have overlapping-sub problems. Memoization is used in order to save time the solutions are stored rather than be recomputed. A solution can be disposed of once we are positive that it will no longer be required, in some cases a solution to a future problem can be computed in advance. 

There are two main approaches for dynamic programming. The first is the bottom up approach. Although it is not always simple to find all of them, any required sub problems are solved in advance and then used to create solutions to larger problems. The other method is the top down approach which is a method that combines memorization and recursion. The main problem is divided into sub problems which are solved and stored for future use.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g2pB_taskb.txt vs g2pB_taskd.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g2pB_taskb.txt vs g3pA_taske.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g2pB_taskb.txt vs g4pC_taskd.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g2pB_taskb.txt vs orig_taskb.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g2pB_taskb.txt vs g0pE_taskc.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g2pB_taskb.txt vs g2pB_taskc.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g2pB_taskb.txt vs g2pC_taske.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g2pB_taskb.txt vs g3pA_taskd.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g2pB_taskb.txt vs g1pA_taskc.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g2pB_taskb.txt vs g3pA_taskb.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g2pB_taskb.txt vs orig_taska.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g2pB_taskb.txt vs orig_taskd.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g2pB_taskb.txt vs g0pA_taskb.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g2pB_taskb.txt vs g0pB_taske.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g2pB_taskb.txt vs g0pD_taskb.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g2pB_taskb.txt vs g0pD_taske.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g2pB_taskb.txt vs g3pB_taskc.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g2pB_taskb.txt vs g3pC_taskc.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g2pB_taskb.txt vs g4pC_taskb.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g2pB_taskb.txt vs g4pC_taske.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g2pB_taskb.txt vs g0pA_taske.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g2pB_taskb.txt vs g0pE_taska.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g2pB_taskb.txt vs g3pA_taska.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g2pB_taskb.txt vs g3pB_taska.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g2pB_taskb.txt vs g4pD_taska.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g2pB_taskb.txt vs orig_taskc.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g2pB_taskb.txt vs g0pA_taskc.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g2pB_taskb.txt vs g2pA_taska.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g2pB_taskb.txt vs g2pC_taskd.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g2pB_taskb.txt vs g4pD_taske.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g2pB_taskb.txt vs g4pD_taskd.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g2pB_taskb.txt vs g0pB_taska.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g2pB_taskb.txt vs g1pB_taske.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g2pB_taskb.txt vs g2pA_taskb.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g2pB_taskb.txt vs g2pA_taskc.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g2pB_taskb.txt vs g1pD_taska.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g2pB_taskb.txt vs g2pB_taska.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g2pB_taskb.txt vs g2pE_taskb.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g2pB_taskb.txt vs g4pE_taskc.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g2pB_taskb.txt vs g0pD_taskd.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g2pB_taskb.txt vs g0pE_taskd.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g2pB_taskb.txt vs g1pA_taskb.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g2pB_taskb.txt vs g1pB_taskb.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g2pB_taskb.txt vs g4pE_taskd.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g2pB_taskb.txt vs g2pC_taska.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g2pB_taskb.txt vs g2pC_taskc.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g2pB_taskb.txt vs g2pE_taska.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g2pB_taskb.txt vs orig_taske.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g2pB_taskb.txt vs g0pB_taskc.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

The vector space model has the following limitations:

g2pB_taskb.txt vs g0pC_taskd.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g2pB_taskb.txt vs g0pC_taske.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g2pB_taskb.txt vs g0pD_taskc.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g2pB_taskb.txt vs g0pC_taskb.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g2pB_taskb.txt vs g2pE_taske.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g2pB_taskb.txt vs g0pC_taska.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g2pB_taskb.txt vs g0pD_taska.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g2pB_taskb.txt vs g4pC_taska.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g2pB_taskb.txt vs g1pB_taskc.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g2pB_taskb.txt vs g1pD_taskc.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g2pB_taskb.txt vs g2pB_taske.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

g2pB_taskb.txt vs g2pE_taskc.txt

The first thing to consider when talking about Google�s PageRank algorithm, is that a PageRank is essentially how important that web page is to the internet. So in essence it is a popularity contest between WebPages.

Originally search engines used highest keyword density, however this could be abused if keyword spamming was implemented. Instead Google uses a system that is based on sites linking to each other, e.g. the more important a site is that is linked to yours the higher your site will become. 

The algorithm Google actually users is based on 4 factors, total number of pages, dampening factor, PageRank of a single page and the number of outbound links. A dampening factor is used to counter random surfers, who get bored and then switch to other pages. This formula is then re-used until the results seem to converge together, to find the PageRank, so it is calculated iteratively.

PageRank is used by Google to measure a popularity of the site and a number between 0-10 is assigned to each webpage depending on their PageRank. This allows Google to calculate a marketing value for different WebPages.

Also it should be noted that the PageRank is periodically updated every 3 to 6 months, this is counter hackers influence on different PageRanks.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g2pB_taskd.txt vs g3pA_taske.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g2pB_taskd.txt vs g4pC_taskd.txt

g2pB_taskd.txt vs orig_taskb.txt

g2pB_taskd.txt vs g0pE_taskc.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g2pB_taskd.txt vs g2pB_taskc.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g2pB_taskd.txt vs g2pC_taske.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g2pB_taskd.txt vs g3pA_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g2pB_taskd.txt vs g1pA_taskc.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g2pB_taskd.txt vs g3pA_taskb.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g2pB_taskd.txt vs orig_taska.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g2pB_taskd.txt vs orig_taskd.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g2pB_taskd.txt vs g0pA_taskb.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g2pB_taskd.txt vs g0pB_taske.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g2pB_taskd.txt vs g0pD_taskb.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g2pB_taskd.txt vs g0pD_taske.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g2pB_taskd.txt vs g3pB_taskc.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g2pB_taskd.txt vs g3pC_taskc.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g2pB_taskd.txt vs g4pC_taskb.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g2pB_taskd.txt vs g4pC_taske.txt

g2pB_taskd.txt vs g0pA_taske.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g2pB_taskd.txt vs g0pE_taska.txt

g2pB_taskd.txt vs g3pA_taska.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g2pB_taskd.txt vs g3pB_taska.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g2pB_taskd.txt vs g4pD_taska.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g2pB_taskd.txt vs orig_taskc.txt

g2pB_taskd.txt vs g0pA_taskc.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g2pB_taskd.txt vs g2pA_taska.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g2pB_taskd.txt vs g2pC_taskd.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g2pB_taskd.txt vs g4pD_taske.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g2pB_taskd.txt vs g4pD_taskd.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g2pB_taskd.txt vs g0pB_taska.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g2pB_taskd.txt vs g1pB_taske.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g2pB_taskd.txt vs g2pA_taskb.txt

g2pB_taskd.txt vs g2pA_taskc.txt

g2pB_taskd.txt vs g1pD_taska.txt

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g2pB_taskd.txt vs g2pB_taska.txt

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g2pB_taskd.txt vs g2pE_taskb.txt

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g2pB_taskd.txt vs g4pE_taskc.txt

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g2pB_taskd.txt vs g0pD_taskd.txt

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g2pB_taskd.txt vs g0pE_taskd.txt

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g2pB_taskd.txt vs g1pA_taskb.txt

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g2pB_taskd.txt vs g1pB_taskb.txt

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g2pB_taskd.txt vs g4pE_taskd.txt

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g2pB_taskd.txt vs g2pC_taska.txt

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g2pB_taskd.txt vs g2pC_taskc.txt

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g2pB_taskd.txt vs g2pE_taska.txt

g2pB_taskd.txt vs orig_taske.txt

g2pB_taskd.txt vs g0pB_taskc.txt

The vector space model has the following limitations:

g2pB_taskd.txt vs g0pC_taskd.txt

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g2pB_taskd.txt vs g0pC_taske.txt

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g2pB_taskd.txt vs g0pD_taskc.txt

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g2pB_taskd.txt vs g0pC_taskb.txt

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g2pB_taskd.txt vs g2pE_taske.txt

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g2pB_taskd.txt vs g0pC_taska.txt

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g2pB_taskd.txt vs g0pD_taska.txt

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g2pB_taskd.txt vs g4pC_taska.txt

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g2pB_taskd.txt vs g1pB_taskc.txt

g2pB_taskd.txt vs g1pD_taskc.txt

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g2pB_taskd.txt vs g2pB_taske.txt

g2pB_taskd.txt vs g2pE_taskc.txt

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g3pA_taske.txt vs g4pC_taskd.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g3pA_taske.txt vs orig_taskb.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g3pA_taske.txt vs g0pE_taskc.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g3pA_taske.txt vs g2pB_taskc.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g3pA_taske.txt vs g2pC_taske.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g3pA_taske.txt vs g3pA_taskd.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g3pA_taske.txt vs g1pA_taskc.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g3pA_taske.txt vs g3pA_taskb.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g3pA_taske.txt vs orig_taska.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g3pA_taske.txt vs orig_taskd.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g3pA_taske.txt vs g0pA_taskb.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g3pA_taske.txt vs g0pB_taske.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g3pA_taske.txt vs g0pD_taskb.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g3pA_taske.txt vs g0pD_taske.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g3pA_taske.txt vs g3pB_taskc.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g3pA_taske.txt vs g3pC_taskc.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g3pA_taske.txt vs g4pC_taskb.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g3pA_taske.txt vs g4pC_taske.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g3pA_taske.txt vs g0pA_taske.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g3pA_taske.txt vs g0pE_taska.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g3pA_taske.txt vs g3pA_taska.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g3pA_taske.txt vs g3pB_taska.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g3pA_taske.txt vs g4pD_taska.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g3pA_taske.txt vs orig_taskc.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g3pA_taske.txt vs g0pA_taskc.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g3pA_taske.txt vs g2pA_taska.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g3pA_taske.txt vs g2pC_taskd.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g3pA_taske.txt vs g4pD_taske.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g3pA_taske.txt vs g4pD_taskd.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g3pA_taske.txt vs g0pB_taska.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g3pA_taske.txt vs g1pB_taske.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g3pA_taske.txt vs g2pA_taskb.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g3pA_taske.txt vs g2pA_taskc.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g3pA_taske.txt vs g1pD_taska.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g3pA_taske.txt vs g2pB_taska.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g3pA_taske.txt vs g2pE_taskb.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g3pA_taske.txt vs g4pE_taskc.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g3pA_taske.txt vs g0pD_taskd.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g3pA_taske.txt vs g0pE_taskd.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g3pA_taske.txt vs g1pA_taskb.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g3pA_taske.txt vs g1pB_taskb.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g3pA_taske.txt vs g4pE_taskd.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g3pA_taske.txt vs g2pC_taska.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g3pA_taske.txt vs g2pC_taskc.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g3pA_taske.txt vs g2pE_taska.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g3pA_taske.txt vs orig_taske.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g3pA_taske.txt vs g0pB_taskc.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

The vector space model has the following limitations:

g3pA_taske.txt vs g0pC_taskd.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g3pA_taske.txt vs g0pC_taske.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g3pA_taske.txt vs g0pD_taskc.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g3pA_taske.txt vs g0pC_taskb.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g3pA_taske.txt vs g2pE_taske.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g3pA_taske.txt vs g0pC_taska.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g3pA_taske.txt vs g0pD_taska.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g3pA_taske.txt vs g4pC_taska.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g3pA_taske.txt vs g1pB_taskc.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g3pA_taske.txt vs g1pD_taskc.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g3pA_taske.txt vs g2pB_taske.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

g3pA_taske.txt vs g2pE_taskc.txt

In the field of computer science, term 'dynamic programming' relates to the style of programming that breaks a large problem down into smaller subproblems, and generally allows for the finding of the optimal solution. When the problem is split into subproblems, these themselves may be split into smaller problems, and so on, until they cannot be reduced any more.
It is also common for dynamic programming to make use of recursion, and the saving of previous results for faster computation later; this also leads to higher efficiency, as calculations are not being redone. For example, when a problem is reduced into sub problems, and those are then reduced further, it may be that there are common subsubproblems, and so only one calculation needs to be done and the result saved to help solve more than one subproblem.
An example of this gain in efficiency is a path-finding problem. If there are two distinct routes in a network of 10 nodes, tagged A to J, then if the two routes share a common section (say, between nodes B and D), the cost of that section should be calculated for the first route and saved. Then, when the second route is being processed, the cost of B to D does not need to be calculated again.
In general, dynamic programming is used on optimisation problems, where the most efficient solution is needed. Areas where this sort of programming is useful is in AI, computer graphics, compression routines, and biomedical applications.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g4pC_taskd.txt vs orig_taskb.txt

g4pC_taskd.txt vs g0pE_taskc.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g4pC_taskd.txt vs g2pB_taskc.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g4pC_taskd.txt vs g2pC_taske.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g4pC_taskd.txt vs g3pA_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g4pC_taskd.txt vs g1pA_taskc.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g4pC_taskd.txt vs g3pA_taskb.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g4pC_taskd.txt vs orig_taska.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g4pC_taskd.txt vs orig_taskd.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g4pC_taskd.txt vs g0pA_taskb.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g4pC_taskd.txt vs g0pB_taske.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g4pC_taskd.txt vs g0pD_taskb.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g4pC_taskd.txt vs g0pD_taske.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g4pC_taskd.txt vs g3pB_taskc.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g4pC_taskd.txt vs g3pC_taskc.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g4pC_taskd.txt vs g4pC_taskb.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g4pC_taskd.txt vs g4pC_taske.txt

g4pC_taskd.txt vs g0pA_taske.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g4pC_taskd.txt vs g0pE_taska.txt

g4pC_taskd.txt vs g3pA_taska.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g4pC_taskd.txt vs g3pB_taska.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g4pC_taskd.txt vs g4pD_taska.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g4pC_taskd.txt vs orig_taskc.txt

g4pC_taskd.txt vs g0pA_taskc.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g4pC_taskd.txt vs g2pA_taska.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g4pC_taskd.txt vs g2pC_taskd.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g4pC_taskd.txt vs g4pD_taske.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g4pC_taskd.txt vs g4pD_taskd.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g4pC_taskd.txt vs g0pB_taska.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g4pC_taskd.txt vs g1pB_taske.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g4pC_taskd.txt vs g2pA_taskb.txt

g4pC_taskd.txt vs g2pA_taskc.txt

g4pC_taskd.txt vs g1pD_taska.txt

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g4pC_taskd.txt vs g2pB_taska.txt

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g4pC_taskd.txt vs g2pE_taskb.txt

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g4pC_taskd.txt vs g4pE_taskc.txt

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g4pC_taskd.txt vs g0pD_taskd.txt

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g4pC_taskd.txt vs g0pE_taskd.txt

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g4pC_taskd.txt vs g1pA_taskb.txt

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g4pC_taskd.txt vs g1pB_taskb.txt

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g4pC_taskd.txt vs g4pE_taskd.txt

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g4pC_taskd.txt vs g2pC_taska.txt

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g4pC_taskd.txt vs g2pC_taskc.txt

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g4pC_taskd.txt vs g2pE_taska.txt

g4pC_taskd.txt vs orig_taske.txt

g4pC_taskd.txt vs g0pB_taskc.txt

The vector space model has the following limitations:

g4pC_taskd.txt vs g0pC_taskd.txt

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g4pC_taskd.txt vs g0pC_taske.txt

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g4pC_taskd.txt vs g0pD_taskc.txt

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g4pC_taskd.txt vs g0pC_taskb.txt

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g4pC_taskd.txt vs g2pE_taske.txt

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g4pC_taskd.txt vs g0pC_taska.txt

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g4pC_taskd.txt vs g0pD_taska.txt

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g4pC_taskd.txt vs g4pC_taska.txt

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g4pC_taskd.txt vs g1pB_taskc.txt

g4pC_taskd.txt vs g1pD_taskc.txt

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g4pC_taskd.txt vs g2pB_taske.txt

g4pC_taskd.txt vs g2pE_taskc.txt

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

orig_taskb.txt vs g0pE_taskc.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

orig_taskb.txt vs g2pB_taskc.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

orig_taskb.txt vs g2pC_taske.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

orig_taskb.txt vs g3pA_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

orig_taskb.txt vs g1pA_taskc.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

orig_taskb.txt vs g3pA_taskb.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

orig_taskb.txt vs orig_taska.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

orig_taskb.txt vs orig_taskd.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

orig_taskb.txt vs g0pA_taskb.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

orig_taskb.txt vs g0pB_taske.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

orig_taskb.txt vs g0pD_taskb.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

orig_taskb.txt vs g0pD_taske.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

orig_taskb.txt vs g3pB_taskc.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

orig_taskb.txt vs g3pC_taskc.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

orig_taskb.txt vs g4pC_taskb.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

orig_taskb.txt vs g4pC_taske.txt

orig_taskb.txt vs g0pA_taske.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

orig_taskb.txt vs g0pE_taska.txt

orig_taskb.txt vs g3pA_taska.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

orig_taskb.txt vs g3pB_taska.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

orig_taskb.txt vs g4pD_taska.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

orig_taskb.txt vs orig_taskc.txt

orig_taskb.txt vs g0pA_taskc.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

orig_taskb.txt vs g2pA_taska.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

orig_taskb.txt vs g2pC_taskd.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

orig_taskb.txt vs g4pD_taske.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

orig_taskb.txt vs g4pD_taskd.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

orig_taskb.txt vs g0pB_taska.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

orig_taskb.txt vs g1pB_taske.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

orig_taskb.txt vs g2pA_taskb.txt

orig_taskb.txt vs g2pA_taskc.txt

orig_taskb.txt vs g1pD_taska.txt

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

orig_taskb.txt vs g2pB_taska.txt

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

orig_taskb.txt vs g2pE_taskb.txt

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

orig_taskb.txt vs g4pE_taskc.txt

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

orig_taskb.txt vs g0pD_taskd.txt

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

orig_taskb.txt vs g0pE_taskd.txt

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

orig_taskb.txt vs g1pA_taskb.txt

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

orig_taskb.txt vs g1pB_taskb.txt

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

orig_taskb.txt vs g4pE_taskd.txt

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

orig_taskb.txt vs g2pC_taska.txt

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

orig_taskb.txt vs g2pC_taskc.txt

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

orig_taskb.txt vs g2pE_taska.txt

orig_taskb.txt vs orig_taske.txt

orig_taskb.txt vs g0pB_taskc.txt

The vector space model has the following limitations:

orig_taskb.txt vs g0pC_taskd.txt

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

orig_taskb.txt vs g0pC_taske.txt

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

orig_taskb.txt vs g0pD_taskc.txt

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

orig_taskb.txt vs g0pC_taskb.txt

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

orig_taskb.txt vs g2pE_taske.txt

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

orig_taskb.txt vs g0pC_taska.txt

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

orig_taskb.txt vs g0pD_taska.txt

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

orig_taskb.txt vs g4pC_taska.txt

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

orig_taskb.txt vs g1pB_taskc.txt

orig_taskb.txt vs g1pD_taskc.txt

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

orig_taskb.txt vs g2pB_taske.txt

orig_taskb.txt vs g2pE_taskc.txt

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g0pE_taskc.txt vs g2pB_taskc.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g0pE_taskc.txt vs g2pC_taske.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g0pE_taskc.txt vs g3pA_taskd.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g0pE_taskc.txt vs g1pA_taskc.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g0pE_taskc.txt vs g3pA_taskb.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g0pE_taskc.txt vs orig_taska.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g0pE_taskc.txt vs orig_taskd.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g0pE_taskc.txt vs g0pA_taskb.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g0pE_taskc.txt vs g0pB_taske.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g0pE_taskc.txt vs g0pD_taskb.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g0pE_taskc.txt vs g0pD_taske.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g0pE_taskc.txt vs g3pB_taskc.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g0pE_taskc.txt vs g3pC_taskc.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g0pE_taskc.txt vs g4pC_taskb.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g0pE_taskc.txt vs g4pC_taske.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g0pE_taskc.txt vs g0pA_taske.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g0pE_taskc.txt vs g0pE_taska.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g0pE_taskc.txt vs g3pA_taska.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g0pE_taskc.txt vs g3pB_taska.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g0pE_taskc.txt vs g4pD_taska.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g0pE_taskc.txt vs orig_taskc.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g0pE_taskc.txt vs g0pA_taskc.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g0pE_taskc.txt vs g2pA_taska.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g0pE_taskc.txt vs g2pC_taskd.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g0pE_taskc.txt vs g4pD_taske.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g0pE_taskc.txt vs g4pD_taskd.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g0pE_taskc.txt vs g0pB_taska.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g0pE_taskc.txt vs g1pB_taske.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g0pE_taskc.txt vs g2pA_taskb.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g0pE_taskc.txt vs g2pA_taskc.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g0pE_taskc.txt vs g1pD_taska.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g0pE_taskc.txt vs g2pB_taska.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g0pE_taskc.txt vs g2pE_taskb.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g0pE_taskc.txt vs g4pE_taskc.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g0pE_taskc.txt vs g0pD_taskd.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g0pE_taskc.txt vs g0pE_taskd.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g0pE_taskc.txt vs g1pA_taskb.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g0pE_taskc.txt vs g1pB_taskb.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g0pE_taskc.txt vs g4pE_taskd.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g0pE_taskc.txt vs g2pC_taska.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g0pE_taskc.txt vs g2pC_taskc.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g0pE_taskc.txt vs g2pE_taska.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g0pE_taskc.txt vs orig_taske.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g0pE_taskc.txt vs g0pB_taskc.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

The vector space model has the following limitations:

g0pE_taskc.txt vs g0pC_taskd.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g0pE_taskc.txt vs g0pC_taske.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g0pE_taskc.txt vs g0pD_taskc.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g0pE_taskc.txt vs g0pC_taskb.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g0pE_taskc.txt vs g2pE_taske.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g0pE_taskc.txt vs g0pC_taska.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g0pE_taskc.txt vs g0pD_taska.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g0pE_taskc.txt vs g4pC_taska.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g0pE_taskc.txt vs g1pB_taskc.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g0pE_taskc.txt vs g1pD_taskc.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g0pE_taskc.txt vs g2pB_taske.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

g0pE_taskc.txt vs g2pE_taskc.txt

The representation of a set of documents as vectors in a common vector space is known as the vector space vector space model and is fundamental to a host of information retrieval (IR) operations including scoring documents on a query, document classification, and document clustering.We first develop the basic ideas underlying vector space scoring; a pivotal step in this development is the view of queries as vectors in the same vector space as the document collection.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g2pB_taskc.txt vs g2pC_taske.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g2pB_taskc.txt vs g3pA_taskd.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g2pB_taskc.txt vs g1pA_taskc.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g2pB_taskc.txt vs g3pA_taskb.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g2pB_taskc.txt vs orig_taska.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g2pB_taskc.txt vs orig_taskd.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g2pB_taskc.txt vs g0pA_taskb.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g2pB_taskc.txt vs g0pB_taske.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g2pB_taskc.txt vs g0pD_taskb.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g2pB_taskc.txt vs g0pD_taske.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g2pB_taskc.txt vs g3pB_taskc.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g2pB_taskc.txt vs g3pC_taskc.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g2pB_taskc.txt vs g4pC_taskb.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g2pB_taskc.txt vs g4pC_taske.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g2pB_taskc.txt vs g0pA_taske.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g2pB_taskc.txt vs g0pE_taska.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g2pB_taskc.txt vs g3pA_taska.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g2pB_taskc.txt vs g3pB_taska.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g2pB_taskc.txt vs g4pD_taska.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g2pB_taskc.txt vs orig_taskc.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g2pB_taskc.txt vs g0pA_taskc.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g2pB_taskc.txt vs g2pA_taska.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g2pB_taskc.txt vs g2pC_taskd.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g2pB_taskc.txt vs g4pD_taske.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g2pB_taskc.txt vs g4pD_taskd.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g2pB_taskc.txt vs g0pB_taska.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g2pB_taskc.txt vs g1pB_taske.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g2pB_taskc.txt vs g2pA_taskb.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g2pB_taskc.txt vs g2pA_taskc.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g2pB_taskc.txt vs g1pD_taska.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g2pB_taskc.txt vs g2pB_taska.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g2pB_taskc.txt vs g2pE_taskb.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g2pB_taskc.txt vs g4pE_taskc.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g2pB_taskc.txt vs g0pD_taskd.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g2pB_taskc.txt vs g0pE_taskd.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g2pB_taskc.txt vs g1pA_taskb.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g2pB_taskc.txt vs g1pB_taskb.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g2pB_taskc.txt vs g4pE_taskd.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g2pB_taskc.txt vs g2pC_taska.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g2pB_taskc.txt vs g2pC_taskc.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g2pB_taskc.txt vs g2pE_taska.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g2pB_taskc.txt vs orig_taske.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g2pB_taskc.txt vs g0pB_taskc.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

The vector space model has the following limitations:

g2pB_taskc.txt vs g0pC_taskd.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g2pB_taskc.txt vs g0pC_taske.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g2pB_taskc.txt vs g0pD_taskc.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g2pB_taskc.txt vs g0pC_taskb.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g2pB_taskc.txt vs g2pE_taske.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g2pB_taskc.txt vs g0pC_taska.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g2pB_taskc.txt vs g0pD_taska.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g2pB_taskc.txt vs g4pC_taska.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g2pB_taskc.txt vs g1pB_taskc.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g2pB_taskc.txt vs g1pD_taskc.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g2pB_taskc.txt vs g2pB_taske.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

g2pB_taskc.txt vs g2pE_taskc.txt

A Vector space model is an algebraic model for representing text documents as vectors of identifiers. A possible use for a vector space model is for retrieval and filtering of information. Other possible uses for vector space models are indexing and also to rank the relevancy of differing documents.
To explain further vector space models, basically a document is characterized by a vector. With each separate term corresponding to the differing dimensions. There has been multiple ways of trying to compute the different possible values for vector space models with the most recognised being the tf-idf weighting.
The differing application has a direct influence on what the definition of the term means. A normal term is usually a single word, keywords or longer phrases. The number of unique words in the vocabulary denotes the dimensionality, if words are used for the terms.
However whilst vector space modelling is useful there are 4 key problems with using it, they are; that the order of the terms are lost, keywords must be precise if searched for, bigger documents have a poor similarity value due to being poorly represented and two documents based on the same topic won�t be associated if term vocabulary differs.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g2pC_taske.txt vs g3pA_taskd.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g2pC_taske.txt vs g1pA_taskc.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g2pC_taske.txt vs g3pA_taskb.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g2pC_taske.txt vs orig_taska.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g2pC_taske.txt vs orig_taskd.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g2pC_taske.txt vs g0pA_taskb.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g2pC_taske.txt vs g0pB_taske.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g2pC_taske.txt vs g0pD_taskb.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g2pC_taske.txt vs g0pD_taske.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g2pC_taske.txt vs g3pB_taskc.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g2pC_taske.txt vs g3pC_taskc.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g2pC_taske.txt vs g4pC_taskb.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g2pC_taske.txt vs g4pC_taske.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g2pC_taske.txt vs g0pA_taske.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g2pC_taske.txt vs g0pE_taska.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g2pC_taske.txt vs g3pA_taska.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g2pC_taske.txt vs g3pB_taska.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g2pC_taske.txt vs g4pD_taska.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g2pC_taske.txt vs orig_taskc.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g2pC_taske.txt vs g0pA_taskc.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g2pC_taske.txt vs g2pA_taska.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g2pC_taske.txt vs g2pC_taskd.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g2pC_taske.txt vs g4pD_taske.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g2pC_taske.txt vs g4pD_taskd.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g2pC_taske.txt vs g0pB_taska.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g2pC_taske.txt vs g1pB_taske.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g2pC_taske.txt vs g2pA_taskb.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g2pC_taske.txt vs g2pA_taskc.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g2pC_taske.txt vs g1pD_taska.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g2pC_taske.txt vs g2pB_taska.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g2pC_taske.txt vs g2pE_taskb.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g2pC_taske.txt vs g4pE_taskc.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g2pC_taske.txt vs g0pD_taskd.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g2pC_taske.txt vs g0pE_taskd.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g2pC_taske.txt vs g1pA_taskb.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g2pC_taske.txt vs g1pB_taskb.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g2pC_taske.txt vs g4pE_taskd.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g2pC_taske.txt vs g2pC_taska.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g2pC_taske.txt vs g2pC_taskc.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g2pC_taske.txt vs g2pE_taska.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g2pC_taske.txt vs orig_taske.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g2pC_taske.txt vs g0pB_taskc.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

The vector space model has the following limitations:

g2pC_taske.txt vs g0pC_taskd.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g2pC_taske.txt vs g0pC_taske.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g2pC_taske.txt vs g0pD_taskc.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g2pC_taske.txt vs g0pC_taskb.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g2pC_taske.txt vs g2pE_taske.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g2pC_taske.txt vs g0pC_taska.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g2pC_taske.txt vs g0pD_taska.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g2pC_taske.txt vs g4pC_taska.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g2pC_taske.txt vs g1pB_taskc.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g2pC_taske.txt vs g1pD_taskc.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g2pC_taske.txt vs g2pB_taske.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

g2pC_taske.txt vs g2pE_taskc.txt

Dynamic programming is a problem-solving method which solves recursive problems. The term is derived from mathematical programming which is commonly referred to as optimisation, hence dynamic programming is an optimal method of solving the problems and takes much less time than naïve methods. 

Dynamic programming uses the properties of optimal substructure, overlapping subproblems and memoization to create an algorithm to solve such problems. Optimal substructure means that the structure of the problem is made up of sub-problems which can be used to find the solution to the problem overall. A problem with overlapping subproblems means that the same subproblems may be used to solve many different larger problems. Each sub-problem is solved by being divided into sub-subproblems, until a case is reached which is solvable in constant time. Memoization stores solutions which have already been computed in order to reduce unnecessary re-computation. 

Dynamic programming can be divided into two main approaches: top-down and bottom-up. The top-down approach breaks the problem into subproblems, which are solved and remembered, using a combination of memoization and recursion. The bottom-up approach solves all subproblems that might be need in advance, and then uses these solutions to build up the solutions to the bigger problem.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g3pA_taskd.txt vs g1pA_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g3pA_taskd.txt vs g3pA_taskb.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g3pA_taskd.txt vs orig_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g3pA_taskd.txt vs orig_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g3pA_taskd.txt vs g0pA_taskb.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g3pA_taskd.txt vs g0pB_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g3pA_taskd.txt vs g0pD_taskb.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g3pA_taskd.txt vs g0pD_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g3pA_taskd.txt vs g3pB_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g3pA_taskd.txt vs g3pC_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g3pA_taskd.txt vs g4pC_taskb.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g3pA_taskd.txt vs g4pC_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g3pA_taskd.txt vs g0pA_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g3pA_taskd.txt vs g0pE_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g3pA_taskd.txt vs g3pA_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g3pA_taskd.txt vs g3pB_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g3pA_taskd.txt vs g4pD_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g3pA_taskd.txt vs orig_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g3pA_taskd.txt vs g0pA_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g3pA_taskd.txt vs g2pA_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g3pA_taskd.txt vs g2pC_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g3pA_taskd.txt vs g4pD_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g3pA_taskd.txt vs g4pD_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g3pA_taskd.txt vs g0pB_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g3pA_taskd.txt vs g1pB_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g3pA_taskd.txt vs g2pA_taskb.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g3pA_taskd.txt vs g2pA_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g3pA_taskd.txt vs g1pD_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g3pA_taskd.txt vs g2pB_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g3pA_taskd.txt vs g2pE_taskb.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g3pA_taskd.txt vs g4pE_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g3pA_taskd.txt vs g0pD_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g3pA_taskd.txt vs g0pE_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g3pA_taskd.txt vs g1pA_taskb.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g3pA_taskd.txt vs g1pB_taskb.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g3pA_taskd.txt vs g4pE_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g3pA_taskd.txt vs g2pC_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g3pA_taskd.txt vs g2pC_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g3pA_taskd.txt vs g2pE_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g3pA_taskd.txt vs orig_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g3pA_taskd.txt vs g0pB_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

The vector space model has the following limitations:

g3pA_taskd.txt vs g0pC_taskd.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g3pA_taskd.txt vs g0pC_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g3pA_taskd.txt vs g0pD_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g3pA_taskd.txt vs g0pC_taskb.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g3pA_taskd.txt vs g2pE_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g3pA_taskd.txt vs g0pC_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g3pA_taskd.txt vs g0pD_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g3pA_taskd.txt vs g4pC_taska.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g3pA_taskd.txt vs g1pB_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g3pA_taskd.txt vs g1pD_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g3pA_taskd.txt vs g2pB_taske.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g3pA_taskd.txt vs g2pE_taskc.txt

Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:

P(A|B) = (P(B | A) x P(A)) / P(B).

Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g1pA_taskc.txt vs g3pA_taskb.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g1pA_taskc.txt vs orig_taska.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g1pA_taskc.txt vs orig_taskd.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g1pA_taskc.txt vs g0pA_taskb.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g1pA_taskc.txt vs g0pB_taske.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g1pA_taskc.txt vs g0pD_taskb.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g1pA_taskc.txt vs g0pD_taske.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g1pA_taskc.txt vs g3pB_taskc.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g1pA_taskc.txt vs g3pC_taskc.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g1pA_taskc.txt vs g4pC_taskb.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g1pA_taskc.txt vs g4pC_taske.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g1pA_taskc.txt vs g0pA_taske.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g1pA_taskc.txt vs g0pE_taska.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g1pA_taskc.txt vs g3pA_taska.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g1pA_taskc.txt vs g3pB_taska.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g1pA_taskc.txt vs g4pD_taska.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g1pA_taskc.txt vs orig_taskc.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g1pA_taskc.txt vs g0pA_taskc.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g1pA_taskc.txt vs g2pA_taska.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g1pA_taskc.txt vs g2pC_taskd.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g1pA_taskc.txt vs g4pD_taske.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g1pA_taskc.txt vs g4pD_taskd.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g1pA_taskc.txt vs g0pB_taska.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g1pA_taskc.txt vs g1pB_taske.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g1pA_taskc.txt vs g2pA_taskb.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g1pA_taskc.txt vs g2pA_taskc.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g1pA_taskc.txt vs g1pD_taska.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g1pA_taskc.txt vs g2pB_taska.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g1pA_taskc.txt vs g2pE_taskb.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g1pA_taskc.txt vs g4pE_taskc.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g1pA_taskc.txt vs g0pD_taskd.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g1pA_taskc.txt vs g0pE_taskd.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g1pA_taskc.txt vs g1pA_taskb.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g1pA_taskc.txt vs g1pB_taskb.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g1pA_taskc.txt vs g4pE_taskd.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g1pA_taskc.txt vs g2pC_taska.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g1pA_taskc.txt vs g2pC_taskc.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g1pA_taskc.txt vs g2pE_taska.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g1pA_taskc.txt vs orig_taske.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g1pA_taskc.txt vs g0pB_taskc.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

The vector space model has the following limitations:

g1pA_taskc.txt vs g0pC_taskd.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g1pA_taskc.txt vs g0pC_taske.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g1pA_taskc.txt vs g0pD_taskc.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g1pA_taskc.txt vs g0pC_taskb.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g1pA_taskc.txt vs g2pE_taske.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g1pA_taskc.txt vs g0pC_taska.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g1pA_taskc.txt vs g0pD_taska.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g1pA_taskc.txt vs g4pC_taska.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g1pA_taskc.txt vs g1pB_taskc.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g1pA_taskc.txt vs g1pD_taskc.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g1pA_taskc.txt vs g2pB_taske.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

g1pA_taskc.txt vs g2pE_taskc.txt

The vector space model is an algebraic model used to represent text documents (and any objects, generally) as vectors of identifiers, for instance index terms. Its applications include information filtering, information retrieval, indexing and relevancy rankings. With reference to this model, documents are represented as vectors. Each dimension corresponds to a separate term. The value of a vector is non-zero if a term occurs in the document. Several different ways have been developed of calculating these values (also known as term weights). One of the best known schemes is tf-idf (term frequency-inverse document frequency) weighting. 

The model can be used to determine the relevancy rankings of documents in a keyword search, using the assumptions of document similarities theory, by comparing the original query vector (where the query is represented as same kind of vector as the documents) and the deviation of angles between each document vector.

The classic vector space model was put forward by Salton, Wong and Yang and is known as term frequency-inverse document frequency model. In this classic model the term specific weights in the document vectors are products of local and global parameters. In a simpler Term Count Model the term specific weights are just the counts of term occurrences and therefore do not include the global parameter.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g3pA_taskb.txt vs orig_taska.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g3pA_taskb.txt vs orig_taskd.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

g3pA_taskb.txt vs g0pA_taskb.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g3pA_taskb.txt vs g0pB_taske.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g3pA_taskb.txt vs g0pD_taskb.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g3pA_taskb.txt vs g0pD_taske.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g3pA_taskb.txt vs g3pB_taskc.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g3pA_taskb.txt vs g3pC_taskc.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g3pA_taskb.txt vs g4pC_taskb.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g3pA_taskb.txt vs g4pC_taske.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g3pA_taskb.txt vs g0pA_taske.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g3pA_taskb.txt vs g0pE_taska.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g3pA_taskb.txt vs g3pA_taska.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g3pA_taskb.txt vs g3pB_taska.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g3pA_taskb.txt vs g4pD_taska.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g3pA_taskb.txt vs orig_taskc.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g3pA_taskb.txt vs g0pA_taskc.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g3pA_taskb.txt vs g2pA_taska.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g3pA_taskb.txt vs g2pC_taskd.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g3pA_taskb.txt vs g4pD_taske.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g3pA_taskb.txt vs g4pD_taskd.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g3pA_taskb.txt vs g0pB_taska.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g3pA_taskb.txt vs g1pB_taske.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g3pA_taskb.txt vs g2pA_taskb.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g3pA_taskb.txt vs g2pA_taskc.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g3pA_taskb.txt vs g1pD_taska.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g3pA_taskb.txt vs g2pB_taska.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g3pA_taskb.txt vs g2pE_taskb.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g3pA_taskb.txt vs g4pE_taskc.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g3pA_taskb.txt vs g0pD_taskd.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g3pA_taskb.txt vs g0pE_taskd.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g3pA_taskb.txt vs g1pA_taskb.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g3pA_taskb.txt vs g1pB_taskb.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g3pA_taskb.txt vs g4pE_taskd.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g3pA_taskb.txt vs g2pC_taska.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g3pA_taskb.txt vs g2pC_taskc.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g3pA_taskb.txt vs g2pE_taska.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g3pA_taskb.txt vs orig_taske.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g3pA_taskb.txt vs g0pB_taskc.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

The vector space model has the following limitations:

g3pA_taskb.txt vs g0pC_taskd.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g3pA_taskb.txt vs g0pC_taske.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g3pA_taskb.txt vs g0pD_taskc.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g3pA_taskb.txt vs g0pC_taskb.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g3pA_taskb.txt vs g2pE_taske.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g3pA_taskb.txt vs g0pC_taska.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g3pA_taskb.txt vs g0pD_taska.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g3pA_taskb.txt vs g4pC_taska.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g3pA_taskb.txt vs g1pB_taskc.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g3pA_taskb.txt vs g1pD_taskc.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g3pA_taskb.txt vs g2pB_taske.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

g3pA_taskb.txt vs g2pE_taskc.txt

The Google search engine uses a link analysis algorithm called PageRank to assign a relative numerical importance to a set of hyperlinked documents, such as the World Wide Web.
For a given page, it's importance (the PageRank value) results from a ballot among all the other pages in the set. For a page to give a vote to another, it must link to it, and so the PageRank depends on the number of incoming links, anf the PageRank of those pages that provide the links. Pages that are linked to by many high ranking pages will themselves obtain a high rank. If a page has no incoming links, there is no support for that page.
The PageRank is a numeric weighting of 0 to 10, and denotes how important a site is in Google's eyes. Like the Richter Scale, the PageRank is a value on a logerithmic scale that is derived from a probability. In addition to the quantity and quality of inbound links,other factors affect the PageRank, such as the number of visits to the page and the search words that are used on the page.
To prevent sites from manipulating or spoofing PageRank, very little details are provided by Google as to what factors actually affect it.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

orig_taska.txt vs orig_taskd.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

orig_taska.txt vs g0pA_taskb.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

orig_taska.txt vs g0pB_taske.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

orig_taska.txt vs g0pD_taskb.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

orig_taska.txt vs g0pD_taske.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

orig_taska.txt vs g3pB_taskc.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

orig_taska.txt vs g3pC_taskc.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

orig_taska.txt vs g4pC_taskb.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

orig_taska.txt vs g4pC_taske.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

orig_taska.txt vs g0pA_taske.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

orig_taska.txt vs g0pE_taska.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

orig_taska.txt vs g3pA_taska.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

orig_taska.txt vs g3pB_taska.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

orig_taska.txt vs g4pD_taska.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

orig_taska.txt vs orig_taskc.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

orig_taska.txt vs g0pA_taskc.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

orig_taska.txt vs g2pA_taska.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

orig_taska.txt vs g2pC_taskd.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

orig_taska.txt vs g4pD_taske.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

orig_taska.txt vs g4pD_taskd.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

orig_taska.txt vs g0pB_taska.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

orig_taska.txt vs g1pB_taske.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

orig_taska.txt vs g2pA_taskb.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

orig_taska.txt vs g2pA_taskc.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

orig_taska.txt vs g1pD_taska.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

orig_taska.txt vs g2pB_taska.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

orig_taska.txt vs g2pE_taskb.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

orig_taska.txt vs g4pE_taskc.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

orig_taska.txt vs g0pD_taskd.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

orig_taska.txt vs g0pE_taskd.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

orig_taska.txt vs g1pA_taskb.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

orig_taska.txt vs g1pB_taskb.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

orig_taska.txt vs g4pE_taskd.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

orig_taska.txt vs g2pC_taska.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

orig_taska.txt vs g2pC_taskc.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

orig_taska.txt vs g2pE_taska.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

orig_taska.txt vs orig_taske.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

orig_taska.txt vs g0pB_taskc.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

The vector space model has the following limitations:

orig_taska.txt vs g0pC_taskd.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

orig_taska.txt vs g0pC_taske.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

orig_taska.txt vs g0pD_taskc.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

orig_taska.txt vs g0pC_taskb.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

orig_taska.txt vs g2pE_taske.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

orig_taska.txt vs g0pC_taska.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

orig_taska.txt vs g0pD_taska.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

orig_taska.txt vs g4pC_taska.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

orig_taska.txt vs g1pB_taskc.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

orig_taska.txt vs g1pD_taskc.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

orig_taska.txt vs g2pB_taske.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

orig_taska.txt vs g2pE_taskc.txt

Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

orig_taskd.txt vs g0pA_taskb.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

orig_taskd.txt vs g0pB_taske.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

orig_taskd.txt vs g0pD_taskb.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

orig_taskd.txt vs g0pD_taske.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

orig_taskd.txt vs g3pB_taskc.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

orig_taskd.txt vs g3pC_taskc.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

orig_taskd.txt vs g4pC_taskb.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

orig_taskd.txt vs g4pC_taske.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

orig_taskd.txt vs g0pA_taske.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

orig_taskd.txt vs g0pE_taska.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

orig_taskd.txt vs g3pA_taska.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

orig_taskd.txt vs g3pB_taska.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

orig_taskd.txt vs g4pD_taska.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

orig_taskd.txt vs orig_taskc.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

orig_taskd.txt vs g0pA_taskc.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

orig_taskd.txt vs g2pA_taska.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

orig_taskd.txt vs g2pC_taskd.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

orig_taskd.txt vs g4pD_taske.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

orig_taskd.txt vs g4pD_taskd.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

orig_taskd.txt vs g0pB_taska.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

orig_taskd.txt vs g1pB_taske.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

orig_taskd.txt vs g2pA_taskb.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

orig_taskd.txt vs g2pA_taskc.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

orig_taskd.txt vs g1pD_taska.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

orig_taskd.txt vs g2pB_taska.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

orig_taskd.txt vs g2pE_taskb.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

orig_taskd.txt vs g4pE_taskc.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

orig_taskd.txt vs g0pD_taskd.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

orig_taskd.txt vs g0pE_taskd.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

orig_taskd.txt vs g1pA_taskb.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

orig_taskd.txt vs g1pB_taskb.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

orig_taskd.txt vs g4pE_taskd.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

orig_taskd.txt vs g2pC_taska.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

orig_taskd.txt vs g2pC_taskc.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

orig_taskd.txt vs g2pE_taska.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

orig_taskd.txt vs orig_taske.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

orig_taskd.txt vs g0pB_taskc.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

The vector space model has the following limitations:

orig_taskd.txt vs g0pC_taskd.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

orig_taskd.txt vs g0pC_taske.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

orig_taskd.txt vs g0pD_taskc.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

orig_taskd.txt vs g0pC_taskb.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

orig_taskd.txt vs g2pE_taske.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

orig_taskd.txt vs g0pC_taska.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

orig_taskd.txt vs g0pD_taska.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

orig_taskd.txt vs g4pC_taska.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

orig_taskd.txt vs g1pB_taskc.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

orig_taskd.txt vs g1pD_taskc.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

orig_taskd.txt vs g2pB_taske.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

orig_taskd.txt vs g2pE_taskc.txt

In probability theory, Bayes' theorem (often called Bayes' law after Rev Thomas Bayes) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)
As a formal theorem, Bayes' theorem is valid in all common interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability:
    P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.
Each term in Bayes' theorem has a conventional name:
    * P(A) is the prior probability or marginal probability of A. It is "prior" in the sense that it does not take into account any information about B.
    * P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
    * P(B|A) is the conditional probability of B given A.
    * P(B) is the prior or marginal probability of B, and acts as a normalizing constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs about observing 'A' are updated by having observed 'B'.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g0pA_taskb.txt vs g0pB_taske.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g0pA_taskb.txt vs g0pD_taskb.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g0pA_taskb.txt vs g0pD_taske.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g0pA_taskb.txt vs g3pB_taskc.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g0pA_taskb.txt vs g3pC_taskc.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g0pA_taskb.txt vs g4pC_taskb.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g0pA_taskb.txt vs g4pC_taske.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g0pA_taskb.txt vs g0pA_taske.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g0pA_taskb.txt vs g0pE_taska.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g0pA_taskb.txt vs g3pA_taska.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g0pA_taskb.txt vs g3pB_taska.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g0pA_taskb.txt vs g4pD_taska.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g0pA_taskb.txt vs orig_taskc.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g0pA_taskb.txt vs g0pA_taskc.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g0pA_taskb.txt vs g2pA_taska.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g0pA_taskb.txt vs g2pC_taskd.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g0pA_taskb.txt vs g4pD_taske.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g0pA_taskb.txt vs g4pD_taskd.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g0pA_taskb.txt vs g0pB_taska.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g0pA_taskb.txt vs g1pB_taske.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g0pA_taskb.txt vs g2pA_taskb.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g0pA_taskb.txt vs g2pA_taskc.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g0pA_taskb.txt vs g1pD_taska.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g0pA_taskb.txt vs g2pB_taska.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g0pA_taskb.txt vs g2pE_taskb.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g0pA_taskb.txt vs g4pE_taskc.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g0pA_taskb.txt vs g0pD_taskd.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g0pA_taskb.txt vs g0pE_taskd.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g0pA_taskb.txt vs g1pA_taskb.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g0pA_taskb.txt vs g1pB_taskb.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g0pA_taskb.txt vs g4pE_taskd.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g0pA_taskb.txt vs g2pC_taska.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g0pA_taskb.txt vs g2pC_taskc.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g0pA_taskb.txt vs g2pE_taska.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g0pA_taskb.txt vs orig_taske.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g0pA_taskb.txt vs g0pB_taskc.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

The vector space model has the following limitations:

g0pA_taskb.txt vs g0pC_taskd.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g0pA_taskb.txt vs g0pC_taske.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g0pA_taskb.txt vs g0pD_taskc.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g0pA_taskb.txt vs g0pC_taskb.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g0pA_taskb.txt vs g2pE_taske.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g0pA_taskb.txt vs g0pC_taska.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g0pA_taskb.txt vs g0pD_taska.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g0pA_taskb.txt vs g4pC_taska.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g0pA_taskb.txt vs g1pB_taskc.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g0pA_taskb.txt vs g1pD_taskc.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g0pA_taskb.txt vs g2pB_taske.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

g0pA_taskb.txt vs g2pE_taskc.txt

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. Google assigns a numeric weighting from 0-10 for each webpage on the Internet; this PageRank? denotes a site’s importance in the eyes of Google.

The PageRank? is derived from a theoretical probability value on a logarithmic scale like the Richter Scale. The PageRank? of a particular page is roughly based upon the quantity of inbound links as well as the PageRank? of the pages providing the links. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank? of E and denoted by PR(E).

It is known that other factors, e.g. relevance of search words on the page and actual visits to the page reported by the Google toolbar also influence the PageRank?. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg (used by Teoma and now Ask.com), the IBM CLEVER project, and the TrustRank? algorithm.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g0pB_taske.txt vs g0pD_taskb.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g0pB_taske.txt vs g0pD_taske.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g0pB_taske.txt vs g3pB_taskc.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g0pB_taske.txt vs g3pC_taskc.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g0pB_taske.txt vs g4pC_taskb.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g0pB_taske.txt vs g4pC_taske.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g0pB_taske.txt vs g0pA_taske.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g0pB_taske.txt vs g0pE_taska.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g0pB_taske.txt vs g3pA_taska.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g0pB_taske.txt vs g3pB_taska.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g0pB_taske.txt vs g4pD_taska.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g0pB_taske.txt vs orig_taskc.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g0pB_taske.txt vs g0pA_taskc.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g0pB_taske.txt vs g2pA_taska.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g0pB_taske.txt vs g2pC_taskd.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g0pB_taske.txt vs g4pD_taske.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g0pB_taske.txt vs g4pD_taskd.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g0pB_taske.txt vs g0pB_taska.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g0pB_taske.txt vs g1pB_taske.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g0pB_taske.txt vs g2pA_taskb.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g0pB_taske.txt vs g2pA_taskc.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g0pB_taske.txt vs g1pD_taska.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g0pB_taske.txt vs g2pB_taska.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g0pB_taske.txt vs g2pE_taskb.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g0pB_taske.txt vs g4pE_taskc.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g0pB_taske.txt vs g0pD_taskd.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g0pB_taske.txt vs g0pE_taskd.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g0pB_taske.txt vs g1pA_taskb.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g0pB_taske.txt vs g1pB_taskb.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g0pB_taske.txt vs g4pE_taskd.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g0pB_taske.txt vs g2pC_taska.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g0pB_taske.txt vs g2pC_taskc.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g0pB_taske.txt vs g2pE_taska.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g0pB_taske.txt vs orig_taske.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g0pB_taske.txt vs g0pB_taskc.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

The vector space model has the following limitations:

g0pB_taske.txt vs g0pC_taskd.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g0pB_taske.txt vs g0pC_taske.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g0pB_taske.txt vs g0pD_taskc.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g0pB_taske.txt vs g0pC_taskb.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g0pB_taske.txt vs g2pE_taske.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g0pB_taske.txt vs g0pC_taska.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g0pB_taske.txt vs g0pD_taska.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g0pB_taske.txt vs g4pC_taska.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g0pB_taske.txt vs g1pB_taskc.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g0pB_taske.txt vs g1pD_taskc.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g0pB_taske.txt vs g2pB_taske.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

g0pB_taske.txt vs g2pE_taskc.txt

1. Break up the problem different smaller subproblems.

2. Recursively use this three-step process to compute the optimal path in the subproblem.

3. Construct an optimal solution, using the computed optimal subproblems, for the original problem.

This process continues recursively, working over the subproblems by dividing them into sub-subproblems and so forth, until a simple case is reached (one that is easily solvable).

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g0pD_taskb.txt vs g0pD_taske.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g0pD_taskb.txt vs g3pB_taskc.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g0pD_taskb.txt vs g3pC_taskc.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g0pD_taskb.txt vs g4pC_taskb.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g0pD_taskb.txt vs g4pC_taske.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g0pD_taskb.txt vs g0pA_taske.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g0pD_taskb.txt vs g0pE_taska.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g0pD_taskb.txt vs g3pA_taska.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g0pD_taskb.txt vs g3pB_taska.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g0pD_taskb.txt vs g4pD_taska.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g0pD_taskb.txt vs orig_taskc.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g0pD_taskb.txt vs g0pA_taskc.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g0pD_taskb.txt vs g2pA_taska.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g0pD_taskb.txt vs g2pC_taskd.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g0pD_taskb.txt vs g4pD_taske.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g0pD_taskb.txt vs g4pD_taskd.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g0pD_taskb.txt vs g0pB_taska.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g0pD_taskb.txt vs g1pB_taske.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g0pD_taskb.txt vs g2pA_taskb.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g0pD_taskb.txt vs g2pA_taskc.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g0pD_taskb.txt vs g1pD_taska.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g0pD_taskb.txt vs g2pB_taska.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g0pD_taskb.txt vs g2pE_taskb.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g0pD_taskb.txt vs g4pE_taskc.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g0pD_taskb.txt vs g0pD_taskd.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g0pD_taskb.txt vs g0pE_taskd.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g0pD_taskb.txt vs g1pA_taskb.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g0pD_taskb.txt vs g1pB_taskb.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g0pD_taskb.txt vs g4pE_taskd.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g0pD_taskb.txt vs g2pC_taska.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g0pD_taskb.txt vs g2pC_taskc.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g0pD_taskb.txt vs g2pE_taska.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g0pD_taskb.txt vs orig_taske.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g0pD_taskb.txt vs g0pB_taskc.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

The vector space model has the following limitations:

g0pD_taskb.txt vs g0pC_taskd.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g0pD_taskb.txt vs g0pC_taske.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g0pD_taskb.txt vs g0pD_taskc.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g0pD_taskb.txt vs g0pC_taskb.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g0pD_taskb.txt vs g2pE_taske.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g0pD_taskb.txt vs g0pC_taska.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g0pD_taskb.txt vs g0pD_taska.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g0pD_taskb.txt vs g4pC_taska.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g0pD_taskb.txt vs g1pB_taskc.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g0pD_taskb.txt vs g1pD_taskc.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g0pD_taskb.txt vs g2pB_taske.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

g0pD_taskb.txt vs g2pE_taskc.txt

PageRank algorithm is patented by Stanford University. It is a link analysis algorithm employed by the Google Internet search engine that assigns a value used to measure the importance to each element of a hyperlinked set of documents, such as the WWW, with the purpose of ” measuring" its relative significance within the set.

Google owns exclusive license rights on the patent from Stanford University. The University received 1.8 million shares in Google in return for use of the patent.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g0pD_taske.txt vs g3pB_taskc.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g0pD_taske.txt vs g3pC_taskc.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g0pD_taske.txt vs g4pC_taskb.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g0pD_taske.txt vs g4pC_taske.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g0pD_taske.txt vs g0pA_taske.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g0pD_taske.txt vs g0pE_taska.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g0pD_taske.txt vs g3pA_taska.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g0pD_taske.txt vs g3pB_taska.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g0pD_taske.txt vs g4pD_taska.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g0pD_taske.txt vs orig_taskc.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g0pD_taske.txt vs g0pA_taskc.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g0pD_taske.txt vs g2pA_taska.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g0pD_taske.txt vs g2pC_taskd.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g0pD_taske.txt vs g4pD_taske.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g0pD_taske.txt vs g4pD_taskd.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g0pD_taske.txt vs g0pB_taska.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g0pD_taske.txt vs g1pB_taske.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g0pD_taske.txt vs g2pA_taskb.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g0pD_taske.txt vs g2pA_taskc.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g0pD_taske.txt vs g1pD_taska.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g0pD_taske.txt vs g2pB_taska.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g0pD_taske.txt vs g2pE_taskb.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g0pD_taske.txt vs g4pE_taskc.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g0pD_taske.txt vs g0pD_taskd.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g0pD_taske.txt vs g0pE_taskd.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g0pD_taske.txt vs g1pA_taskb.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g0pD_taske.txt vs g1pB_taskb.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g0pD_taske.txt vs g4pE_taskd.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g0pD_taske.txt vs g2pC_taska.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g0pD_taske.txt vs g2pC_taskc.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g0pD_taske.txt vs g2pE_taska.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g0pD_taske.txt vs orig_taske.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g0pD_taske.txt vs g0pB_taskc.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

The vector space model has the following limitations:

g0pD_taske.txt vs g0pC_taskd.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g0pD_taske.txt vs g0pC_taske.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g0pD_taske.txt vs g0pD_taskc.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g0pD_taske.txt vs g0pC_taskb.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g0pD_taske.txt vs g2pE_taske.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g0pD_taske.txt vs g0pC_taska.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g0pD_taske.txt vs g0pD_taska.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g0pD_taske.txt vs g4pC_taska.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g0pD_taske.txt vs g1pB_taskc.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g0pD_taske.txt vs g1pD_taskc.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g0pD_taske.txt vs g2pB_taske.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

g0pD_taske.txt vs g2pE_taskc.txt

Dynamic programming (DP) is an extremely powerful, general tool for solving optimization difficulties on left-right-ordered item, for example character strings. It is similar to divide and conquer, however is differentiated as its subproblems are not independent. It is easily applicable, in relative terms, once understood. However until one has witnessed enough examples, it looks like magic.

DP minimizes computation by solving subproblems from the base upwards, storing solution to a subproblem when it is initially conquered, and looking up the solution when the subproblem is experienced for a second time.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g3pB_taskc.txt vs g3pC_taskc.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g3pB_taskc.txt vs g4pC_taskb.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g3pB_taskc.txt vs g4pC_taske.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g3pB_taskc.txt vs g0pA_taske.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g3pB_taskc.txt vs g0pE_taska.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g3pB_taskc.txt vs g3pA_taska.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g3pB_taskc.txt vs g3pB_taska.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g3pB_taskc.txt vs g4pD_taska.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g3pB_taskc.txt vs orig_taskc.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g3pB_taskc.txt vs g0pA_taskc.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g3pB_taskc.txt vs g2pA_taska.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g3pB_taskc.txt vs g2pC_taskd.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g3pB_taskc.txt vs g4pD_taske.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g3pB_taskc.txt vs g4pD_taskd.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g3pB_taskc.txt vs g0pB_taska.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g3pB_taskc.txt vs g1pB_taske.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g3pB_taskc.txt vs g2pA_taskb.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g3pB_taskc.txt vs g2pA_taskc.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g3pB_taskc.txt vs g1pD_taska.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g3pB_taskc.txt vs g2pB_taska.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g3pB_taskc.txt vs g2pE_taskb.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g3pB_taskc.txt vs g4pE_taskc.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g3pB_taskc.txt vs g0pD_taskd.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g3pB_taskc.txt vs g0pE_taskd.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g3pB_taskc.txt vs g1pA_taskb.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g3pB_taskc.txt vs g1pB_taskb.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g3pB_taskc.txt vs g4pE_taskd.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g3pB_taskc.txt vs g2pC_taska.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g3pB_taskc.txt vs g2pC_taskc.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g3pB_taskc.txt vs g2pE_taska.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g3pB_taskc.txt vs orig_taske.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g3pB_taskc.txt vs g0pB_taskc.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

The vector space model has the following limitations:

g3pB_taskc.txt vs g0pC_taskd.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g3pB_taskc.txt vs g0pC_taske.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g3pB_taskc.txt vs g0pD_taskc.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g3pB_taskc.txt vs g0pC_taskb.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g3pB_taskc.txt vs g2pE_taske.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g3pB_taskc.txt vs g0pC_taska.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g3pB_taskc.txt vs g0pD_taska.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g3pB_taskc.txt vs g4pC_taska.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g3pB_taskc.txt vs g1pB_taskc.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g3pB_taskc.txt vs g1pD_taskc.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g3pB_taskc.txt vs g2pB_taske.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

g3pB_taskc.txt vs g2pE_taskc.txt

There are a large number of models used in solving the problem of Information Retrieval and they are all based on one of three mathematical bases: set theory, algebra and probabilistic.  The vector space model is one of these methods, and it is an algebraic model.

In the vector space model a document is represented as a vector.  Within this vector, each dimension corresponds to a separate term (where a term is typically a single word, keyword or phrase.)  If the term doesn’t occur within the document, the value in the vector is zero.  If a term occurs in the document, its value is non-zero.

To calculate how relevant each document is in a keyword search the cosine value of the angle between the vectors is easier to calculate instead of the actual angle.

The vector space model, however, is not without its limitations: they have small similarity values, long documents are poorly represented; the order of words does not matter; false positive matches may be brought about by terms contained within words themselves; and documents that should match but use different semantics may return false negative matches.   There are a number of other models that are based on or extend the vector space model, and these are designed to try to eradicate these problems.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g3pC_taskc.txt vs g4pC_taskb.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g3pC_taskc.txt vs g4pC_taske.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g3pC_taskc.txt vs g0pA_taske.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g3pC_taskc.txt vs g0pE_taska.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g3pC_taskc.txt vs g3pA_taska.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g3pC_taskc.txt vs g3pB_taska.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g3pC_taskc.txt vs g4pD_taska.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g3pC_taskc.txt vs orig_taskc.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g3pC_taskc.txt vs g0pA_taskc.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g3pC_taskc.txt vs g2pA_taska.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g3pC_taskc.txt vs g2pC_taskd.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g3pC_taskc.txt vs g4pD_taske.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g3pC_taskc.txt vs g4pD_taskd.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g3pC_taskc.txt vs g0pB_taska.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g3pC_taskc.txt vs g1pB_taske.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g3pC_taskc.txt vs g2pA_taskb.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g3pC_taskc.txt vs g2pA_taskc.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g3pC_taskc.txt vs g1pD_taska.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g3pC_taskc.txt vs g2pB_taska.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g3pC_taskc.txt vs g2pE_taskb.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g3pC_taskc.txt vs g4pE_taskc.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g3pC_taskc.txt vs g0pD_taskd.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g3pC_taskc.txt vs g0pE_taskd.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g3pC_taskc.txt vs g1pA_taskb.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g3pC_taskc.txt vs g1pB_taskb.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g3pC_taskc.txt vs g4pE_taskd.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g3pC_taskc.txt vs g2pC_taska.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g3pC_taskc.txt vs g2pC_taskc.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g3pC_taskc.txt vs g2pE_taska.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g3pC_taskc.txt vs orig_taske.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g3pC_taskc.txt vs g0pB_taskc.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

The vector space model has the following limitations:

g3pC_taskc.txt vs g0pC_taskd.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g3pC_taskc.txt vs g0pC_taske.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g3pC_taskc.txt vs g0pD_taskc.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g3pC_taskc.txt vs g0pC_taskb.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g3pC_taskc.txt vs g2pE_taske.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g3pC_taskc.txt vs g0pC_taska.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g3pC_taskc.txt vs g0pD_taska.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g3pC_taskc.txt vs g4pC_taska.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g3pC_taskc.txt vs g1pB_taskc.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g3pC_taskc.txt vs g1pD_taskc.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g3pC_taskc.txt vs g2pB_taske.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

g3pC_taskc.txt vs g2pE_taskc.txt

Using the vector space model for Information Retrieval models all pages
and queries as high-dimensional sparse vectors. Each item in the vector
represents a different keyword.

The similiarity betweeen two pages or a query and a page can be computed
using the dot product formula to find the cosine between them. This
represents the angle between them, but in n-dimensional space. Results
will range from -1 to 1, with 1 being a close match. Normally the vectors
will not have any negative values, so results will always be greater than
or equal to 0. The cosine is computed using: cos A = (|a||b|)/(a.b)

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g4pC_taskb.txt vs g4pC_taske.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g4pC_taskb.txt vs g0pA_taske.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g4pC_taskb.txt vs g0pE_taska.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g4pC_taskb.txt vs g3pA_taska.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g4pC_taskb.txt vs g3pB_taska.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g4pC_taskb.txt vs g4pD_taska.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g4pC_taskb.txt vs orig_taskc.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g4pC_taskb.txt vs g0pA_taskc.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g4pC_taskb.txt vs g2pA_taska.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g4pC_taskb.txt vs g2pC_taskd.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g4pC_taskb.txt vs g4pD_taske.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g4pC_taskb.txt vs g4pD_taskd.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g4pC_taskb.txt vs g0pB_taska.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g4pC_taskb.txt vs g1pB_taske.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g4pC_taskb.txt vs g2pA_taskb.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g4pC_taskb.txt vs g2pA_taskc.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g4pC_taskb.txt vs g1pD_taska.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g4pC_taskb.txt vs g2pB_taska.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g4pC_taskb.txt vs g2pE_taskb.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g4pC_taskb.txt vs g4pE_taskc.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g4pC_taskb.txt vs g0pD_taskd.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g4pC_taskb.txt vs g0pE_taskd.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g4pC_taskb.txt vs g1pA_taskb.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g4pC_taskb.txt vs g1pB_taskb.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g4pC_taskb.txt vs g4pE_taskd.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g4pC_taskb.txt vs g2pC_taska.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g4pC_taskb.txt vs g2pC_taskc.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g4pC_taskb.txt vs g2pE_taska.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g4pC_taskb.txt vs orig_taske.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g4pC_taskb.txt vs g0pB_taskc.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

The vector space model has the following limitations:

g4pC_taskb.txt vs g0pC_taskd.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g4pC_taskb.txt vs g0pC_taske.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g4pC_taskb.txt vs g0pD_taskc.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g4pC_taskb.txt vs g0pC_taskb.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g4pC_taskb.txt vs g2pE_taske.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g4pC_taskb.txt vs g0pC_taska.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g4pC_taskb.txt vs g0pD_taska.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g4pC_taskb.txt vs g4pC_taska.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g4pC_taskb.txt vs g1pB_taskc.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g4pC_taskb.txt vs g1pD_taskc.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g4pC_taskb.txt vs g2pB_taske.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

g4pC_taskb.txt vs g2pE_taskc.txt

Since the develop of the Web 2.0, Google as one of the most popular search engine in the world,  there are many algorithms in the web search. Accordingly, implementations of link analysis algorithms will typical discount such “internal” links. The word computer can be exploited by web search engines such as Google. Thus, the web is just like a graph, and the PageRank, which is our first technique for analysing the link which is  assigns to every node in
the web graph a numerical score between 0 and 1. Since the PageRank is the most important algorithms which is used in the Google engine. For example, there are four pages group: A, B, C and D. If every page link to A, then  A’s PageRank value shoule be the total value of  B, C and D .
PR(A) = PR(B) + PR(C) + PR(D)
Moreover, there is a q = 0.15 which is be use in the web page, like the general algorithm below:
 
However, the disadvantage is of PageRank algorithm is that the renew system is too slow.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g4pC_taske.txt vs g0pA_taske.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g4pC_taske.txt vs g0pE_taska.txt

g4pC_taske.txt vs g3pA_taska.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g4pC_taske.txt vs g3pB_taska.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g4pC_taske.txt vs g4pD_taska.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g4pC_taske.txt vs orig_taskc.txt

g4pC_taske.txt vs g0pA_taskc.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g4pC_taske.txt vs g2pA_taska.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g4pC_taske.txt vs g2pC_taskd.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g4pC_taske.txt vs g4pD_taske.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g4pC_taske.txt vs g4pD_taskd.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g4pC_taske.txt vs g0pB_taska.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g4pC_taske.txt vs g1pB_taske.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g4pC_taske.txt vs g2pA_taskb.txt

g4pC_taske.txt vs g2pA_taskc.txt

g4pC_taske.txt vs g1pD_taska.txt

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g4pC_taske.txt vs g2pB_taska.txt

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g4pC_taske.txt vs g2pE_taskb.txt

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g4pC_taske.txt vs g4pE_taskc.txt

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g4pC_taske.txt vs g0pD_taskd.txt

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g4pC_taske.txt vs g0pE_taskd.txt

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g4pC_taske.txt vs g1pA_taskb.txt

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g4pC_taske.txt vs g1pB_taskb.txt

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g4pC_taske.txt vs g4pE_taskd.txt

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g4pC_taske.txt vs g2pC_taska.txt

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g4pC_taske.txt vs g2pC_taskc.txt

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g4pC_taske.txt vs g2pE_taska.txt

g4pC_taske.txt vs orig_taske.txt

g4pC_taske.txt vs g0pB_taskc.txt

The vector space model has the following limitations:

g4pC_taske.txt vs g0pC_taskd.txt

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g4pC_taske.txt vs g0pC_taske.txt

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g4pC_taske.txt vs g0pD_taskc.txt

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g4pC_taske.txt vs g0pC_taskb.txt

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g4pC_taske.txt vs g2pE_taske.txt

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g4pC_taske.txt vs g0pC_taska.txt

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g4pC_taske.txt vs g0pD_taska.txt

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g4pC_taske.txt vs g4pC_taska.txt

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g4pC_taske.txt vs g1pB_taskc.txt

g4pC_taske.txt vs g1pD_taskc.txt

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g4pC_taske.txt vs g2pB_taske.txt

g4pC_taske.txt vs g2pE_taskc.txt

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g0pA_taske.txt vs g0pE_taska.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g0pA_taske.txt vs g3pA_taska.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g0pA_taske.txt vs g3pB_taska.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g0pA_taske.txt vs g4pD_taska.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g0pA_taske.txt vs orig_taskc.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g0pA_taske.txt vs g0pA_taskc.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g0pA_taske.txt vs g2pA_taska.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g0pA_taske.txt vs g2pC_taskd.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g0pA_taske.txt vs g4pD_taske.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g0pA_taske.txt vs g4pD_taskd.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g0pA_taske.txt vs g0pB_taska.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g0pA_taske.txt vs g1pB_taske.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g0pA_taske.txt vs g2pA_taskb.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g0pA_taske.txt vs g2pA_taskc.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g0pA_taske.txt vs g1pD_taska.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g0pA_taske.txt vs g2pB_taska.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g0pA_taske.txt vs g2pE_taskb.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g0pA_taske.txt vs g4pE_taskc.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g0pA_taske.txt vs g0pD_taskd.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g0pA_taske.txt vs g0pE_taskd.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g0pA_taske.txt vs g1pA_taskb.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g0pA_taske.txt vs g1pB_taskb.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g0pA_taske.txt vs g4pE_taskd.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g0pA_taske.txt vs g2pC_taska.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g0pA_taske.txt vs g2pC_taskc.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g0pA_taske.txt vs g2pE_taska.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g0pA_taske.txt vs orig_taske.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g0pA_taske.txt vs g0pB_taskc.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

The vector space model has the following limitations:

g0pA_taske.txt vs g0pC_taskd.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g0pA_taske.txt vs g0pC_taske.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g0pA_taske.txt vs g0pD_taskc.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g0pA_taske.txt vs g0pC_taskb.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g0pA_taske.txt vs g2pE_taske.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g0pA_taske.txt vs g0pC_taska.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g0pA_taske.txt vs g0pD_taska.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g0pA_taske.txt vs g4pC_taska.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g0pA_taske.txt vs g1pB_taskc.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g0pA_taske.txt vs g1pD_taskc.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g0pA_taske.txt vs g2pB_taske.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

g0pA_taske.txt vs g2pE_taskc.txt

Dynamic Programming is an algorithm design technique used for optimisation problems, such as minimising or maximising. Like divide and conquer, Dynamic Programming solves problems by combining solutions to sub-problems. However, unlike divide and conquer, sub-problems are not always independent as sub-problems may share sub-sub-problems but solution to one sub-problem may not affect the solutions to other sub-problems of the same problem.

There are four steps in Dynamic Programming:

1. Characterise structure of an optimal solution.

2. Define value of optimal solution recursively.

3. Compute optimal solution values either top-down with caching or bottom-up in a table.

4. Construct an optimal solution from computed values.

An example of the type of problem for which Dynamic Programming may be used is: given two sequences, X=(x1,...,xm) and Y=(y1,...,yn) find a common subsequence whose length is maximum.

Dynamic Programming reduces computation by solving sub-problems in a bottom-up fashion and by storing solution to a sub-problem the first time it is solved. Also, looking up the solution when a sub-problem is encountered again helps reduce computation. However, the key in Dynamic Programming is to determine the structure of optimal solutions.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g0pE_taska.txt vs g3pA_taska.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g0pE_taska.txt vs g3pB_taska.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g0pE_taska.txt vs g4pD_taska.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g0pE_taska.txt vs orig_taskc.txt

g0pE_taska.txt vs g0pA_taskc.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g0pE_taska.txt vs g2pA_taska.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g0pE_taska.txt vs g2pC_taskd.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g0pE_taska.txt vs g4pD_taske.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g0pE_taska.txt vs g4pD_taskd.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g0pE_taska.txt vs g0pB_taska.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g0pE_taska.txt vs g1pB_taske.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g0pE_taska.txt vs g2pA_taskb.txt

g0pE_taska.txt vs g2pA_taskc.txt

g0pE_taska.txt vs g1pD_taska.txt

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g0pE_taska.txt vs g2pB_taska.txt

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g0pE_taska.txt vs g2pE_taskb.txt

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g0pE_taska.txt vs g4pE_taskc.txt

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g0pE_taska.txt vs g0pD_taskd.txt

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g0pE_taska.txt vs g0pE_taskd.txt

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g0pE_taska.txt vs g1pA_taskb.txt

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g0pE_taska.txt vs g1pB_taskb.txt

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g0pE_taska.txt vs g4pE_taskd.txt

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g0pE_taska.txt vs g2pC_taska.txt

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g0pE_taska.txt vs g2pC_taskc.txt

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g0pE_taska.txt vs g2pE_taska.txt

g0pE_taska.txt vs orig_taske.txt

g0pE_taska.txt vs g0pB_taskc.txt

The vector space model has the following limitations:

g0pE_taska.txt vs g0pC_taskd.txt

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g0pE_taska.txt vs g0pC_taske.txt

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g0pE_taska.txt vs g0pD_taskc.txt

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g0pE_taska.txt vs g0pC_taskb.txt

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g0pE_taska.txt vs g2pE_taske.txt

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g0pE_taska.txt vs g0pC_taska.txt

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g0pE_taska.txt vs g0pD_taska.txt

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g0pE_taska.txt vs g4pC_taska.txt

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g0pE_taska.txt vs g1pB_taskc.txt

g0pE_taska.txt vs g1pD_taskc.txt

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g0pE_taska.txt vs g2pB_taske.txt

g0pE_taska.txt vs g2pE_taskc.txt

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g3pA_taska.txt vs g3pB_taska.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g3pA_taska.txt vs g4pD_taska.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g3pA_taska.txt vs orig_taskc.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g3pA_taska.txt vs g0pA_taskc.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g3pA_taska.txt vs g2pA_taska.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g3pA_taska.txt vs g2pC_taskd.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g3pA_taska.txt vs g4pD_taske.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g3pA_taska.txt vs g4pD_taskd.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g3pA_taska.txt vs g0pB_taska.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g3pA_taska.txt vs g1pB_taske.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g3pA_taska.txt vs g2pA_taskb.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g3pA_taska.txt vs g2pA_taskc.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g3pA_taska.txt vs g1pD_taska.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g3pA_taska.txt vs g2pB_taska.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g3pA_taska.txt vs g2pE_taskb.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g3pA_taska.txt vs g4pE_taskc.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g3pA_taska.txt vs g0pD_taskd.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g3pA_taska.txt vs g0pE_taskd.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g3pA_taska.txt vs g1pA_taskb.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g3pA_taska.txt vs g1pB_taskb.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g3pA_taska.txt vs g4pE_taskd.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g3pA_taska.txt vs g2pC_taska.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g3pA_taska.txt vs g2pC_taskc.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g3pA_taska.txt vs g2pE_taska.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g3pA_taska.txt vs orig_taske.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g3pA_taska.txt vs g0pB_taskc.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

The vector space model has the following limitations:

g3pA_taska.txt vs g0pC_taskd.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g3pA_taska.txt vs g0pC_taske.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g3pA_taska.txt vs g0pD_taskc.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g3pA_taska.txt vs g0pC_taskb.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g3pA_taska.txt vs g2pE_taske.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g3pA_taska.txt vs g0pC_taska.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g3pA_taska.txt vs g0pD_taska.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g3pA_taska.txt vs g4pC_taska.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g3pA_taska.txt vs g1pB_taskc.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g3pA_taska.txt vs g1pD_taskc.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g3pA_taska.txt vs g2pB_taske.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

g3pA_taska.txt vs g2pE_taskc.txt

In object-oriented programming, inheritance is the ability to specify one class to be a subclass of another; this leads to a hierarchy of classes, with the child classes inheriting and specialising - and sometimes adding to - the functionality and data structures of the parent classes. The hierarchy that is formed is also useful for the organisation of classes and objects, as it defines a relationship between the child and the parent (the child class is a �kind of� the parent class). Inheritance is useful for situations where several classes share common features, such as needed functions or data variables. In addition to this, child classes can be referenced in terms of their parent classes, which can be useful when storing large data structures of objects of several classes, which can all be referenced as one base class. Inheritance is a core aspect of object-oriented programming, and is available in some form or another in most, if not all, object oriented languages available today. Most of these languages provide an �extend� keyword, which is used to subclass another. Also, the functions and data variables that are inherited by the subclasses can be controlled through the use of visibility modifiers.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g3pB_taska.txt vs g4pD_taska.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g3pB_taska.txt vs orig_taskc.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g3pB_taska.txt vs g0pA_taskc.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g3pB_taska.txt vs g2pA_taska.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g3pB_taska.txt vs g2pC_taskd.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g3pB_taska.txt vs g4pD_taske.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g3pB_taska.txt vs g4pD_taskd.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g3pB_taska.txt vs g0pB_taska.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g3pB_taska.txt vs g1pB_taske.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g3pB_taska.txt vs g2pA_taskb.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g3pB_taska.txt vs g2pA_taskc.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g3pB_taska.txt vs g1pD_taska.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g3pB_taska.txt vs g2pB_taska.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g3pB_taska.txt vs g2pE_taskb.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g3pB_taska.txt vs g4pE_taskc.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g3pB_taska.txt vs g0pD_taskd.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g3pB_taska.txt vs g0pE_taskd.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g3pB_taska.txt vs g1pA_taskb.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g3pB_taska.txt vs g1pB_taskb.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g3pB_taska.txt vs g4pE_taskd.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g3pB_taska.txt vs g2pC_taska.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g3pB_taska.txt vs g2pC_taskc.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g3pB_taska.txt vs g2pE_taska.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g3pB_taska.txt vs orig_taske.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g3pB_taska.txt vs g0pB_taskc.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

The vector space model has the following limitations:

g3pB_taska.txt vs g0pC_taskd.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g3pB_taska.txt vs g0pC_taske.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g3pB_taska.txt vs g0pD_taskc.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g3pB_taska.txt vs g0pC_taskb.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g3pB_taska.txt vs g2pE_taske.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g3pB_taska.txt vs g0pC_taska.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g3pB_taska.txt vs g0pD_taska.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g3pB_taska.txt vs g4pC_taska.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g3pB_taska.txt vs g1pB_taskc.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g3pB_taska.txt vs g1pD_taskc.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g3pB_taska.txt vs g2pB_taske.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

g3pB_taska.txt vs g2pE_taskc.txt

Inheritance is a concept in Object Oriented programming where a child- or sub-class inherits characteristics from a parent- or super-class.  The concept takes its name from genetic inheritance where a child can inherit genetic characteristics from its parents.

Inheritance, at its simplest, allows programmers to model a relationship where one object is a kind of another.  For instance two classes, one representing an undergraduate student and another representing a post-graduate student could both be said to belong to a more generalised class representing all students.  Similarly, we could say that dogs and cats are two kinds of animal, or that bridges and skyscrapers are two types of man-made structure.

Subclasses are said to extend or specialise their superclasses.  Attributes (variables) and behaviours (functions) that are common between classes can be included in the definition of the superclass, leaving the subclass definitions containing only the attributes and behaviours that are unique to that class.

Inheritance can be used to create a multiple level architecture of classes.  In such an architecture even the bottom-most subclasses inherit all of the attributes and behaviours that are defined in the very top-most superclasses.  This can save the programmer time because it renders unnecessary a lot of code duplication.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g4pD_taska.txt vs orig_taskc.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g4pD_taska.txt vs g0pA_taskc.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g4pD_taska.txt vs g2pA_taska.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g4pD_taska.txt vs g2pC_taskd.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g4pD_taska.txt vs g4pD_taske.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g4pD_taska.txt vs g4pD_taskd.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g4pD_taska.txt vs g0pB_taska.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g4pD_taska.txt vs g1pB_taske.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g4pD_taska.txt vs g2pA_taskb.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g4pD_taska.txt vs g2pA_taskc.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g4pD_taska.txt vs g1pD_taska.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g4pD_taska.txt vs g2pB_taska.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g4pD_taska.txt vs g2pE_taskb.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g4pD_taska.txt vs g4pE_taskc.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g4pD_taska.txt vs g0pD_taskd.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g4pD_taska.txt vs g0pE_taskd.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g4pD_taska.txt vs g1pA_taskb.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g4pD_taska.txt vs g1pB_taskb.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g4pD_taska.txt vs g4pE_taskd.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g4pD_taska.txt vs g2pC_taska.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g4pD_taska.txt vs g2pC_taskc.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g4pD_taska.txt vs g2pE_taska.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g4pD_taska.txt vs orig_taske.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g4pD_taska.txt vs g0pB_taskc.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

The vector space model has the following limitations:

g4pD_taska.txt vs g0pC_taskd.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g4pD_taska.txt vs g0pC_taske.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g4pD_taska.txt vs g0pD_taskc.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g4pD_taska.txt vs g0pC_taskb.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g4pD_taska.txt vs g2pE_taske.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g4pD_taska.txt vs g0pC_taska.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g4pD_taska.txt vs g0pD_taska.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g4pD_taska.txt vs g4pC_taska.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g4pD_taska.txt vs g1pB_taskc.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g4pD_taska.txt vs g1pD_taskc.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g4pD_taska.txt vs g2pB_taske.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

g4pD_taska.txt vs g2pE_taskc.txt

The idea of inheritance in OOP refers to the formation of new classes with the already existing classes. The concept of inheritance was basically formulated for Simula in 1967.
As a result, the newly created inherited or derived classes inherit the properties and behavior of the classes from which they are derived. These original classes are either called base classes or sometimes referred to as ancestor classes.
The idea of inheritance is to reuse the existing code with little or no modification at all.
The basic support provided by inheritance is that it represents by categorization in computer languages. The power mechanism number of information processing that is crucial to human learning by the means of generalization and cognitive economy is called categorization. Where generalization if the knowledge of specific entities and is applied to a wider group provided that belongs relation can be created. On the other hand cognitive economy is where less information needs to be stored about each specific entity except for some particularities.
There are examples where we can have modules with similar interfaces. The advantage that inheritance provides is that it makes such modules share a lot of code which consequently reduces the complexity of the program.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

orig_taskc.txt vs g0pA_taskc.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

orig_taskc.txt vs g2pA_taska.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

orig_taskc.txt vs g2pC_taskd.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

orig_taskc.txt vs g4pD_taske.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

orig_taskc.txt vs g4pD_taskd.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

orig_taskc.txt vs g0pB_taska.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

orig_taskc.txt vs g1pB_taske.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

orig_taskc.txt vs g2pA_taskb.txt

orig_taskc.txt vs g2pA_taskc.txt

orig_taskc.txt vs g1pD_taska.txt

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

orig_taskc.txt vs g2pB_taska.txt

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

orig_taskc.txt vs g2pE_taskb.txt

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

orig_taskc.txt vs g4pE_taskc.txt

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

orig_taskc.txt vs g0pD_taskd.txt

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

orig_taskc.txt vs g0pE_taskd.txt

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

orig_taskc.txt vs g1pA_taskb.txt

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

orig_taskc.txt vs g1pB_taskb.txt

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

orig_taskc.txt vs g4pE_taskd.txt

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

orig_taskc.txt vs g2pC_taska.txt

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

orig_taskc.txt vs g2pC_taskc.txt

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

orig_taskc.txt vs g2pE_taska.txt

orig_taskc.txt vs orig_taske.txt

orig_taskc.txt vs g0pB_taskc.txt

The vector space model has the following limitations:

orig_taskc.txt vs g0pC_taskd.txt

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

orig_taskc.txt vs g0pC_taske.txt

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

orig_taskc.txt vs g0pD_taskc.txt

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

orig_taskc.txt vs g0pC_taskb.txt

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

orig_taskc.txt vs g2pE_taske.txt

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

orig_taskc.txt vs g0pC_taska.txt

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

orig_taskc.txt vs g0pD_taska.txt

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

orig_taskc.txt vs g4pC_taska.txt

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

orig_taskc.txt vs g1pB_taskc.txt

orig_taskc.txt vs g1pD_taskc.txt

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

orig_taskc.txt vs g2pB_taske.txt

orig_taskc.txt vs g2pE_taskc.txt

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g0pA_taskc.txt vs g2pA_taska.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g0pA_taskc.txt vs g2pC_taskd.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g0pA_taskc.txt vs g4pD_taske.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g0pA_taskc.txt vs g4pD_taskd.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g0pA_taskc.txt vs g0pB_taska.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g0pA_taskc.txt vs g1pB_taske.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g0pA_taskc.txt vs g2pA_taskb.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g0pA_taskc.txt vs g2pA_taskc.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g0pA_taskc.txt vs g1pD_taska.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g0pA_taskc.txt vs g2pB_taska.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g0pA_taskc.txt vs g2pE_taskb.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g0pA_taskc.txt vs g4pE_taskc.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g0pA_taskc.txt vs g0pD_taskd.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g0pA_taskc.txt vs g0pE_taskd.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g0pA_taskc.txt vs g1pA_taskb.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g0pA_taskc.txt vs g1pB_taskb.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g0pA_taskc.txt vs g4pE_taskd.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g0pA_taskc.txt vs g2pC_taska.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g0pA_taskc.txt vs g2pC_taskc.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g0pA_taskc.txt vs g2pE_taska.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g0pA_taskc.txt vs orig_taske.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g0pA_taskc.txt vs g0pB_taskc.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

The vector space model has the following limitations:

g0pA_taskc.txt vs g0pC_taskd.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g0pA_taskc.txt vs g0pC_taske.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g0pA_taskc.txt vs g0pD_taskc.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g0pA_taskc.txt vs g0pC_taskb.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g0pA_taskc.txt vs g2pE_taske.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g0pA_taskc.txt vs g0pC_taska.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g0pA_taskc.txt vs g0pD_taska.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g0pA_taskc.txt vs g4pC_taska.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g0pA_taskc.txt vs g1pB_taskc.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g0pA_taskc.txt vs g1pD_taskc.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g0pA_taskc.txt vs g2pB_taske.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

g0pA_taskc.txt vs g2pE_taskc.txt

The vector space model (also called, term vector model) is an algebraic model used to represent text documents, as well as any objects in general, as vectors of identifiers. It is used in information retrieval and was first used in the SMART Information Retrieval System.

A document is represented as a vector and each dimension corresponds to a separate term. If a term appears in the document then its value in the vector is non-zero. Many different ways of calculating these values, also known as (term) weights, have been developed. One of the best known methods is called tf-idf weighting.

The definition of term depends on the application but generally terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary, which is the number of distinct words occurring in the corpus.

The vector space model has several disadvantages. Firstly, long documents are represented badly because they have poor similarity values. Secondly, search keywords must accurately match document terms and substrings of words might result in a "false-positive match". Thirdly, documents with similar context but different term vocabulary will not be associated, resulting in a "false-negative match". Finally, the order in which the terms appear in the document is lost in the vector space representation.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g2pA_taska.txt vs g2pC_taskd.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g2pA_taska.txt vs g4pD_taske.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g2pA_taska.txt vs g4pD_taskd.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g2pA_taska.txt vs g0pB_taska.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g2pA_taska.txt vs g1pB_taske.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g2pA_taska.txt vs g2pA_taskb.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g2pA_taska.txt vs g2pA_taskc.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g2pA_taska.txt vs g1pD_taska.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g2pA_taska.txt vs g2pB_taska.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g2pA_taska.txt vs g2pE_taskb.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g2pA_taska.txt vs g4pE_taskc.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g2pA_taska.txt vs g0pD_taskd.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g2pA_taska.txt vs g0pE_taskd.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g2pA_taska.txt vs g1pA_taskb.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g2pA_taska.txt vs g1pB_taskb.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g2pA_taska.txt vs g4pE_taskd.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g2pA_taska.txt vs g2pC_taska.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g2pA_taska.txt vs g2pC_taskc.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g2pA_taska.txt vs g2pE_taska.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g2pA_taska.txt vs orig_taske.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g2pA_taska.txt vs g0pB_taskc.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

The vector space model has the following limitations:

g2pA_taska.txt vs g0pC_taskd.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g2pA_taska.txt vs g0pC_taske.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g2pA_taska.txt vs g0pD_taskc.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g2pA_taska.txt vs g0pC_taskb.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g2pA_taska.txt vs g2pE_taske.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g2pA_taska.txt vs g0pC_taska.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g2pA_taska.txt vs g0pD_taska.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g2pA_taska.txt vs g4pC_taska.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g2pA_taska.txt vs g1pB_taskc.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g2pA_taska.txt vs g1pD_taskc.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g2pA_taska.txt vs g2pB_taske.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

g2pA_taska.txt vs g2pE_taskc.txt

Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a �Transport� class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to �extend� the Transport class, as they will have additional characteristics which they don�t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of �is toilet engaged�.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a �toilet engaged� function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you�d have a train and aeroplane, which would inherit characteristics from both super classes.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g2pC_taskd.txt vs g4pD_taske.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g2pC_taskd.txt vs g4pD_taskd.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g2pC_taskd.txt vs g0pB_taska.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g2pC_taskd.txt vs g1pB_taske.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g2pC_taskd.txt vs g2pA_taskb.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g2pC_taskd.txt vs g2pA_taskc.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g2pC_taskd.txt vs g1pD_taska.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g2pC_taskd.txt vs g2pB_taska.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g2pC_taskd.txt vs g2pE_taskb.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g2pC_taskd.txt vs g4pE_taskc.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g2pC_taskd.txt vs g0pD_taskd.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g2pC_taskd.txt vs g0pE_taskd.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g2pC_taskd.txt vs g1pA_taskb.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g2pC_taskd.txt vs g1pB_taskb.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g2pC_taskd.txt vs g4pE_taskd.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g2pC_taskd.txt vs g2pC_taska.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g2pC_taskd.txt vs g2pC_taskc.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g2pC_taskd.txt vs g2pE_taska.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g2pC_taskd.txt vs orig_taske.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g2pC_taskd.txt vs g0pB_taskc.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

The vector space model has the following limitations:

g2pC_taskd.txt vs g0pC_taskd.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g2pC_taskd.txt vs g0pC_taske.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g2pC_taskd.txt vs g0pD_taskc.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g2pC_taskd.txt vs g0pC_taskb.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g2pC_taskd.txt vs g2pE_taske.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g2pC_taskd.txt vs g0pC_taska.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g2pC_taskd.txt vs g0pD_taska.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g2pC_taskd.txt vs g4pC_taska.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g2pC_taskd.txt vs g1pB_taskc.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g2pC_taskd.txt vs g1pD_taskc.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g2pC_taskd.txt vs g2pB_taske.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

g2pC_taskd.txt vs g2pE_taskc.txt

In probability theory, Bayes' theorem relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations.

Bayes' theorem is expressed mathematically as:

P(A|B) = (P(B|A)P(A))/P(B)

where P(A|B) is the conditional probability of A given B, P(A) is the prior probability of A, P(B) is the prior probability of B, and P(B|A) is the conditional probability of B given A. 

Bayes' theorem relates the conditional and marginal probabilities of two random events P(A) and P(B), and is valid in all common interpretations of probability. For example, in a school in made up of 3/5 boys and 2/5 girls, the girls wear skirts of trousers in equal numbers and the boys all wear trousers. If a student is observed from a distance wearing trousers, Bayes theorem can be used to determine the probability of this student being a girl. 

P(A) is the probability of the student being a girl (which is 2/5). 
P(B|A) is the probability of the student wearing trousers given that the student is a girl, which is 0.5 
P(B) is the probability of a random student wearing trousers, which can be calculated as P(B) = P(B|A)P(A) + P(B|A')P(A') where ' denotes a complementary event, which is 0.8. 
Therefore the probability using the formula is 0.25. 

Bayes theorem is often used to compute posterior probabilities given observations, for instance the probability that a proposed medical diagnosis is correct, given certain observed symptoms.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g4pD_taske.txt vs g4pD_taskd.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g4pD_taske.txt vs g0pB_taska.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g4pD_taske.txt vs g1pB_taske.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g4pD_taske.txt vs g2pA_taskb.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g4pD_taske.txt vs g2pA_taskc.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g4pD_taske.txt vs g1pD_taska.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g4pD_taske.txt vs g2pB_taska.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g4pD_taske.txt vs g2pE_taskb.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g4pD_taske.txt vs g4pE_taskc.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g4pD_taske.txt vs g0pD_taskd.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g4pD_taske.txt vs g0pE_taskd.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g4pD_taske.txt vs g1pA_taskb.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g4pD_taske.txt vs g1pB_taskb.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g4pD_taske.txt vs g4pE_taskd.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g4pD_taske.txt vs g2pC_taska.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g4pD_taske.txt vs g2pC_taskc.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g4pD_taske.txt vs g2pE_taska.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g4pD_taske.txt vs orig_taske.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g4pD_taske.txt vs g0pB_taskc.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

The vector space model has the following limitations:

g4pD_taske.txt vs g0pC_taskd.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g4pD_taske.txt vs g0pC_taske.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g4pD_taske.txt vs g0pD_taskc.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g4pD_taske.txt vs g0pC_taskb.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g4pD_taske.txt vs g2pE_taske.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g4pD_taske.txt vs g0pC_taska.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g4pD_taske.txt vs g0pD_taska.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g4pD_taske.txt vs g4pC_taska.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g4pD_taske.txt vs g1pB_taskc.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g4pD_taske.txt vs g1pD_taskc.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g4pD_taske.txt vs g2pB_taske.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

g4pD_taske.txt vs g2pE_taskc.txt

Dynamic programming is a method of providing solutions to potential problems exhibiting the properties of overlapping sub problems and optimal structure. This is highly used in dynamic programming. The advantage being the less time consumption in comparison to other amateur methods.
It has to be kept in mind that the term programming in the field has got nothing to do with computer programming at all. On the other hand it is derived from the term mathematical programming which is a similar word used for optimization. Here by meaning that a program can be an optimal plan for the produced action. The typical example could be of a finalized schedule of events at an exhibition. This leads to the concept of programming being a helper in finding an acceptable plan of action, which can also be termed as an algorithm
The subproblems are, themselves, solved by dividing them into sub-subproblems, and so on, until we reach some simple case that is solvable in constant time.
Overlapping subproblems means that the same subproblems are used to solve many different larger problems. Example could be of Fibonacci sequence; F3 = F1 + F2 and F4 = F2 + F3 � computing each number involves computing F2. Because both F3 and F4 are needed to compute F5, a naive approach to computing F5 may end up computing F2 twice or more. It means that whenever we encounter with  overlapping subproblems, a naive approach may waste to,e recomputing optimal solutions to the already solved subproblems.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g4pD_taskd.txt vs g0pB_taska.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g4pD_taskd.txt vs g1pB_taske.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g4pD_taskd.txt vs g2pA_taskb.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g4pD_taskd.txt vs g2pA_taskc.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g4pD_taskd.txt vs g1pD_taska.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g4pD_taskd.txt vs g2pB_taska.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g4pD_taskd.txt vs g2pE_taskb.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g4pD_taskd.txt vs g4pE_taskc.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g4pD_taskd.txt vs g0pD_taskd.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g4pD_taskd.txt vs g0pE_taskd.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g4pD_taskd.txt vs g1pA_taskb.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g4pD_taskd.txt vs g1pB_taskb.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g4pD_taskd.txt vs g4pE_taskd.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g4pD_taskd.txt vs g2pC_taska.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g4pD_taskd.txt vs g2pC_taskc.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g4pD_taskd.txt vs g2pE_taska.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g4pD_taskd.txt vs orig_taske.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g4pD_taskd.txt vs g0pB_taskc.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

The vector space model has the following limitations:

g4pD_taskd.txt vs g0pC_taskd.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g4pD_taskd.txt vs g0pC_taske.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g4pD_taskd.txt vs g0pD_taskc.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g4pD_taskd.txt vs g0pC_taskb.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g4pD_taskd.txt vs g2pE_taske.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g4pD_taskd.txt vs g0pC_taska.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g4pD_taskd.txt vs g0pD_taska.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g4pD_taskd.txt vs g4pC_taska.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g4pD_taskd.txt vs g1pB_taskc.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g4pD_taskd.txt vs g1pD_taskc.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g4pD_taskd.txt vs g2pB_taske.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

g4pD_taskd.txt vs g2pE_taskc.txt

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. Bayes' Theorem is a theorem of probability theory originally stated by the Reverend Thomas Bayes. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence. It has been used in a wide variety of contexts, ranging from marine biology to the development of "Bayesian" spam blockers for email systems. In the philosophy of science, it has been used to try to clarify the relationship between theory and evidence. Many insights in the philosophy of science involving confirmation, falsification, the relation between science and pseudosience, and other topics can be made more precise, and sometimes extended or corrected, by using Bayes' Theorem. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight � that a hypothesis is confirmed by any body of data that its truth renders probable � is the cornerstone of all subjectivist methodology.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g0pB_taska.txt vs g1pB_taske.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g0pB_taska.txt vs g2pA_taskb.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g0pB_taska.txt vs g2pA_taskc.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g0pB_taska.txt vs g1pD_taska.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g0pB_taska.txt vs g2pB_taska.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g0pB_taska.txt vs g2pE_taskb.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g0pB_taska.txt vs g4pE_taskc.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g0pB_taska.txt vs g0pD_taskd.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g0pB_taska.txt vs g0pE_taskd.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g0pB_taska.txt vs g1pA_taskb.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g0pB_taska.txt vs g1pB_taskb.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g0pB_taska.txt vs g4pE_taskd.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g0pB_taska.txt vs g2pC_taska.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g0pB_taska.txt vs g2pC_taskc.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g0pB_taska.txt vs g2pE_taska.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g0pB_taska.txt vs orig_taske.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g0pB_taska.txt vs g0pB_taskc.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

The vector space model has the following limitations:

g0pB_taska.txt vs g0pC_taskd.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g0pB_taska.txt vs g0pC_taske.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g0pB_taska.txt vs g0pD_taskc.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g0pB_taska.txt vs g0pC_taskb.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g0pB_taska.txt vs g2pE_taske.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g0pB_taska.txt vs g0pC_taska.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g0pB_taska.txt vs g0pD_taska.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g0pB_taska.txt vs g4pC_taska.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g0pB_taska.txt vs g1pB_taskc.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g0pB_taska.txt vs g1pD_taskc.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g0pB_taska.txt vs g2pB_taske.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

g0pB_taska.txt vs g2pE_taskc.txt

Inheritance is a basic concept in object oriented programming. It models the reuse of existing class code in new classes – the “is a kind of” relationship.

For example, a house is a kind of building; similarly, an office block is a kind of building. Both house and office block will inherit certain characteristics from buildings, but also have their own personal characteristics – a house may have a number of occupants, whereas an office block will have a number of offices. However, these personal characteristics don't apply to all types of buildings.

In this example, the building would be considered the superclass – it contains general characteristics for other objects to inherit – and the house and office block are both subclasses – they are specific types and specialise the characteristics of the superclass.

Java allows object inheritance. When one class inherits from another class, all the public variables and methods are available to the subclass.

public class Shape {

  private Color colour;

  public void setColour(Color newColour){

    colour = newColour;

  }

}

public class Circle extends Shape {

  private int radius;

  public void setRadius(int newRadius){

    radius = newRadius;

  }

}

In this example, the Circle class is a subclass of the Shape class. The Shape class provides a public setColour method, which will be available to the Circle class and other subclasses of Shape. However, the private variable colour (as defined in the Shape class) will not be available for direct manipulation by the Circle class because it is not inherited. The Circle class specialises the Shape class, which means that setRadius is available to the Circle class and all subclasses of Circle, but it isn't available to the superclass Shape.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g1pB_taske.txt vs g2pA_taskb.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g1pB_taske.txt vs g2pA_taskc.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g1pB_taske.txt vs g1pD_taska.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g1pB_taske.txt vs g2pB_taska.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g1pB_taske.txt vs g2pE_taskb.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g1pB_taske.txt vs g4pE_taskc.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g1pB_taske.txt vs g0pD_taskd.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g1pB_taske.txt vs g0pE_taskd.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g1pB_taske.txt vs g1pA_taskb.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g1pB_taske.txt vs g1pB_taskb.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g1pB_taske.txt vs g4pE_taskd.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g1pB_taske.txt vs g2pC_taska.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g1pB_taske.txt vs g2pC_taskc.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g1pB_taske.txt vs g2pE_taska.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g1pB_taske.txt vs orig_taske.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g1pB_taske.txt vs g0pB_taskc.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

The vector space model has the following limitations:

g1pB_taske.txt vs g0pC_taskd.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g1pB_taske.txt vs g0pC_taske.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g1pB_taske.txt vs g0pD_taskc.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g1pB_taske.txt vs g0pC_taskb.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g1pB_taske.txt vs g2pE_taske.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g1pB_taske.txt vs g0pC_taska.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g1pB_taske.txt vs g0pD_taska.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g1pB_taske.txt vs g4pC_taska.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g1pB_taske.txt vs g1pB_taskc.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g1pB_taske.txt vs g1pD_taskc.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g1pB_taske.txt vs g2pB_taske.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

g1pB_taske.txt vs g2pE_taskc.txt

In mathematics and computer science, dynamic programming is a method of solving problems that exhibit the properties of overlapping sub problems and optimal substructure. The term was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he had refined this to the modern meaning. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. The word "programming" in "dynamic programming" has no particular connection to computer programming at all, and instead comes from the term "mathematical programming", a synonym for optimization. Thus, the "program" is the optimal plan for action that is produced. For instance, a finalized schedule of events at an exhibition is sometimes called a program. Programming, in this sense, means finding an acceptable plan of action, an algorithm.
Dynamic programming usually takes one of two approaches, the top-down approach, the problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together and the bottom-up approach, all sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. This approach is slightly better in stack space and number of function calls, but it is sometimes not intuitive to figure out all the sub problems needed for solving the given problem.
Some programming languages can automatically memorize the result of a function call with a particular set of arguments, in order to speed up call-by-name. Some languages make it possible portably (e.g. Scheme, Common Lisp or Perl), some need special extensions.This is only possible for a referentially transparent function.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g2pA_taskb.txt vs g2pA_taskc.txt

g2pA_taskb.txt vs g1pD_taska.txt

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g2pA_taskb.txt vs g2pB_taska.txt

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g2pA_taskb.txt vs g2pE_taskb.txt

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g2pA_taskb.txt vs g4pE_taskc.txt

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g2pA_taskb.txt vs g0pD_taskd.txt

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g2pA_taskb.txt vs g0pE_taskd.txt

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g2pA_taskb.txt vs g1pA_taskb.txt

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g2pA_taskb.txt vs g1pB_taskb.txt

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g2pA_taskb.txt vs g4pE_taskd.txt

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g2pA_taskb.txt vs g2pC_taska.txt

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g2pA_taskb.txt vs g2pC_taskc.txt

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g2pA_taskb.txt vs g2pE_taska.txt

g2pA_taskb.txt vs orig_taske.txt

g2pA_taskb.txt vs g0pB_taskc.txt

The vector space model has the following limitations:

g2pA_taskb.txt vs g0pC_taskd.txt

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g2pA_taskb.txt vs g0pC_taske.txt

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g2pA_taskb.txt vs g0pD_taskc.txt

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g2pA_taskb.txt vs g0pC_taskb.txt

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g2pA_taskb.txt vs g2pE_taske.txt

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g2pA_taskb.txt vs g0pC_taska.txt

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g2pA_taskb.txt vs g0pD_taska.txt

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g2pA_taskb.txt vs g4pC_taska.txt

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g2pA_taskb.txt vs g1pB_taskc.txt

g2pA_taskb.txt vs g1pD_taskc.txt

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g2pA_taskb.txt vs g2pB_taske.txt

g2pA_taskb.txt vs g2pE_taskc.txt

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g2pA_taskc.txt vs g1pD_taska.txt

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g2pA_taskc.txt vs g2pB_taska.txt

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g2pA_taskc.txt vs g2pE_taskb.txt

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g2pA_taskc.txt vs g4pE_taskc.txt

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g2pA_taskc.txt vs g0pD_taskd.txt

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g2pA_taskc.txt vs g0pE_taskd.txt

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g2pA_taskc.txt vs g1pA_taskb.txt

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g2pA_taskc.txt vs g1pB_taskb.txt

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g2pA_taskc.txt vs g4pE_taskd.txt

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g2pA_taskc.txt vs g2pC_taska.txt

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g2pA_taskc.txt vs g2pC_taskc.txt

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g2pA_taskc.txt vs g2pE_taska.txt

g2pA_taskc.txt vs orig_taske.txt

g2pA_taskc.txt vs g0pB_taskc.txt

The vector space model has the following limitations:

g2pA_taskc.txt vs g0pC_taskd.txt

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g2pA_taskc.txt vs g0pC_taske.txt

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g2pA_taskc.txt vs g0pD_taskc.txt

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g2pA_taskc.txt vs g0pC_taskb.txt

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g2pA_taskc.txt vs g2pE_taske.txt

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g2pA_taskc.txt vs g0pC_taska.txt

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g2pA_taskc.txt vs g0pD_taska.txt

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g2pA_taskc.txt vs g4pC_taska.txt

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g2pA_taskc.txt vs g1pB_taskc.txt

g2pA_taskc.txt vs g1pD_taskc.txt

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g2pA_taskc.txt vs g2pB_taske.txt

g2pA_taskc.txt vs g2pE_taskc.txt

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g1pD_taska.txt vs g2pB_taska.txt

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g1pD_taska.txt vs g2pE_taskb.txt

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g1pD_taska.txt vs g4pE_taskc.txt

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g1pD_taska.txt vs g0pD_taskd.txt

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g1pD_taska.txt vs g0pE_taskd.txt

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g1pD_taska.txt vs g1pA_taskb.txt

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g1pD_taska.txt vs g1pB_taskb.txt

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g1pD_taska.txt vs g4pE_taskd.txt

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g1pD_taska.txt vs g2pC_taska.txt

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g1pD_taska.txt vs g2pC_taskc.txt

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g1pD_taska.txt vs g2pE_taska.txt

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g1pD_taska.txt vs orig_taske.txt

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g1pD_taska.txt vs g0pB_taskc.txt

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

The vector space model has the following limitations:

g1pD_taska.txt vs g0pC_taskd.txt

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g1pD_taska.txt vs g0pC_taske.txt

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g1pD_taska.txt vs g0pD_taskc.txt

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g1pD_taska.txt vs g0pC_taskb.txt

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g1pD_taska.txt vs g2pE_taske.txt

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g1pD_taska.txt vs g0pC_taska.txt

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g1pD_taska.txt vs g0pD_taska.txt

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g1pD_taska.txt vs g4pC_taska.txt

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g1pD_taska.txt vs g1pB_taskc.txt

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g1pD_taska.txt vs g1pD_taskc.txt

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g1pD_taska.txt vs g2pB_taske.txt

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

g1pD_taska.txt vs g2pE_taskc.txt

Inheritance is a method of forming new classes using predefined classes. The new classes are called derived classes and they inherit the behaviours and attributes of the base classes. It was intended to allow existing code to be used again with minimal or no alteration. It also offers support for representation by categorization in computer languages; this is a powerful mechanism of information processing, vital to human learning by means of generalization and cognitive economy. Inheritance is occasionally referred to as generalization due to the fact that is-a relationships represent a hierarchy between classes of objects. Inheritance has the advantage of reducing the complexity of a program since modules with very similar interfaces can share lots of code. Due to this, inheritance has another view called polymorphism, where many sections of code are being controlled by some shared control code. Inheritance is normally achieved by overriding one or more methods exposed by ancestor, or by creating new methods on top of those exposed by an ancestor. Inheritance has a variety of uses. Each different use focuses on different properties, for example the external behaviour of objects, internal structure of an object, inheritance hierarchy structure, or software engineering properties of inheritance. Occasionally it is advantageous to differentiate between these uses, as it is not necessarily noticeable from context.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g2pB_taska.txt vs g2pE_taskb.txt

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g2pB_taska.txt vs g4pE_taskc.txt

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g2pB_taska.txt vs g0pD_taskd.txt

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g2pB_taska.txt vs g0pE_taskd.txt

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g2pB_taska.txt vs g1pA_taskb.txt

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g2pB_taska.txt vs g1pB_taskb.txt

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g2pB_taska.txt vs g4pE_taskd.txt

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g2pB_taska.txt vs g2pC_taska.txt

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g2pB_taska.txt vs g2pC_taskc.txt

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g2pB_taska.txt vs g2pE_taska.txt

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g2pB_taska.txt vs orig_taske.txt

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g2pB_taska.txt vs g0pB_taskc.txt

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

The vector space model has the following limitations:

g2pB_taska.txt vs g0pC_taskd.txt

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g2pB_taska.txt vs g0pC_taske.txt

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g2pB_taska.txt vs g0pD_taskc.txt

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g2pB_taska.txt vs g0pC_taskb.txt

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g2pB_taska.txt vs g2pE_taske.txt

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g2pB_taska.txt vs g0pC_taska.txt

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g2pB_taska.txt vs g0pD_taska.txt

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g2pB_taska.txt vs g4pC_taska.txt

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g2pB_taska.txt vs g1pB_taskc.txt

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g2pB_taska.txt vs g1pD_taskc.txt

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g2pB_taska.txt vs g2pB_taske.txt

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

g2pB_taska.txt vs g2pE_taskc.txt

 Inheritance is an important feature in object orientated programming. This is because it allows new classes to be made that extend previous classes and to go into more detail. 

This is carried out by allowing the new class to reuse the existing class methods and variables, whilst also creating class specific methods and variables. This means that the new class, the subclass, is a more specialised version of the original, or superclass.

Because of this it means that the subclass can use all the public methods and variables from the superclass; however any private methods or variables are still private. 

Also it should be noted that a class can only extend one class, e.g. can only be a subclass to one superclass. However a superclass can have more then one subclass and a class can both be a subclass and a superclass. If this occurs then all of the non-private methods and variables can be used by the most specialised class.

This means that inheritance is used when types have common factors and these would be put into the superclass. Then the subclass/es then extend these to add more detail. An example of this could be using a superclass of employee and then to have two subclasses called fulltime and part time. As employee could have name, address and other details whilst full time could just have salary and part time could work out the salary from part time hours worked, as the full time members of staff wouldn�t need these.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g2pE_taskb.txt vs g4pE_taskc.txt

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g2pE_taskb.txt vs g0pD_taskd.txt

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g2pE_taskb.txt vs g0pE_taskd.txt

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g2pE_taskb.txt vs g1pA_taskb.txt

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g2pE_taskb.txt vs g1pB_taskb.txt

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g2pE_taskb.txt vs g4pE_taskd.txt

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g2pE_taskb.txt vs g2pC_taska.txt

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g2pE_taskb.txt vs g2pC_taskc.txt

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g2pE_taskb.txt vs g2pE_taska.txt

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g2pE_taskb.txt vs orig_taske.txt

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g2pE_taskb.txt vs g0pB_taskc.txt

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

The vector space model has the following limitations:

g2pE_taskb.txt vs g0pC_taskd.txt

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g2pE_taskb.txt vs g0pC_taske.txt

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g2pE_taskb.txt vs g0pD_taskc.txt

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g2pE_taskb.txt vs g0pC_taskb.txt

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g2pE_taskb.txt vs g2pE_taske.txt

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g2pE_taskb.txt vs g0pC_taska.txt

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g2pE_taskb.txt vs g0pD_taska.txt

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g2pE_taskb.txt vs g4pC_taska.txt

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g2pE_taskb.txt vs g1pB_taskc.txt

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g2pE_taskb.txt vs g1pD_taskc.txt

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g2pE_taskb.txt vs g2pB_taske.txt

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

g2pE_taskb.txt vs g2pE_taskc.txt

PageRank is a link analysis algorithm that is used by search engine such as Google Internet that assigns a numerical weighting to every element of a hyperlinked set of documents, like the World Wide Web, with the hope of "measuring" the relative importance held in the set. The algorithm may be applied to any numbr of entities with reciprocal quotations and references. The weight taking a numerical value which assigns to any given element E is also known as the PageRank of E and is denoted by PR(E).
A trademark of Google has the name "PageRank"  and this process has been patented (U.S. Patent 6,285,999 ). Nevertheless, the patent is assigned to the University of Stanford and not to Google. Google has exclusive license rights on the patent from the University of Stanford and the university received 1.8 million shares in Google in exchange for use of the patent; the in the year 2005, shares were sold for $336 million.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g4pE_taskc.txt vs g0pD_taskd.txt

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g4pE_taskc.txt vs g0pE_taskd.txt

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g4pE_taskc.txt vs g1pA_taskb.txt

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g4pE_taskc.txt vs g1pB_taskb.txt

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g4pE_taskc.txt vs g4pE_taskd.txt

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g4pE_taskc.txt vs g2pC_taska.txt

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g4pE_taskc.txt vs g2pC_taskc.txt

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g4pE_taskc.txt vs g2pE_taska.txt

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g4pE_taskc.txt vs orig_taske.txt

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g4pE_taskc.txt vs g0pB_taskc.txt

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

The vector space model has the following limitations:

g4pE_taskc.txt vs g0pC_taskd.txt

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g4pE_taskc.txt vs g0pC_taske.txt

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g4pE_taskc.txt vs g0pD_taskc.txt

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g4pE_taskc.txt vs g0pC_taskb.txt

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g4pE_taskc.txt vs g2pE_taske.txt

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g4pE_taskc.txt vs g0pC_taska.txt

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g4pE_taskc.txt vs g0pD_taska.txt

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g4pE_taskc.txt vs g4pC_taska.txt

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g4pE_taskc.txt vs g1pB_taskc.txt

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g4pE_taskc.txt vs g1pD_taskc.txt

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g4pE_taskc.txt vs g2pB_taske.txt

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

g4pE_taskc.txt vs g2pE_taskc.txt

The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If the words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary A document is represented as a vector. Each dimensions corresponds to a separate terms. If a term occurs in the document, its value in the vector is non-zero.
Relevancy rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.
LIMITATION:
There is some limitation of vector space model.
Models based on and extending the vector space model include:
�	Generalized vector space model.
�	(enhanced) Topic-based Vector Space Model [1] (eTVSM) � Extends the vector space model by removing the constraint that the term-vectors be orthogonal. In contrast to the generalized vector space model the (enhanced) Topic-based Vector Space Model does not depend on concurrence-based similarities between terms. The enhancement of the enhanced Topic-based Vector Space Model  (compared to the not enhanced one) is a proposal on how to derive term-vectors from an Ontology.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g0pD_taskd.txt vs g0pE_taskd.txt

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g0pD_taskd.txt vs g1pA_taskb.txt

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g0pD_taskd.txt vs g1pB_taskb.txt

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g0pD_taskd.txt vs g4pE_taskd.txt

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g0pD_taskd.txt vs g2pC_taska.txt

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g0pD_taskd.txt vs g2pC_taskc.txt

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g0pD_taskd.txt vs g2pE_taska.txt

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g0pD_taskd.txt vs orig_taske.txt

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g0pD_taskd.txt vs g0pB_taskc.txt

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

The vector space model has the following limitations:

g0pD_taskd.txt vs g0pC_taskd.txt

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g0pD_taskd.txt vs g0pC_taske.txt

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g0pD_taskd.txt vs g0pD_taskc.txt

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g0pD_taskd.txt vs g0pC_taskb.txt

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g0pD_taskd.txt vs g2pE_taske.txt

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g0pD_taskd.txt vs g0pC_taska.txt

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g0pD_taskd.txt vs g0pD_taska.txt

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g0pD_taskd.txt vs g4pC_taska.txt

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g0pD_taskd.txt vs g1pB_taskc.txt

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g0pD_taskd.txt vs g1pD_taskc.txt

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g0pD_taskd.txt vs g2pB_taske.txt

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

g0pD_taskd.txt vs g2pE_taskc.txt

Baye’s theorm in connection with conditional probabilities is of fundamental importance, since it permits a calculation of PROB(AB) from PROB(BA). Statistical information that is often gathered in great volume can therefore be avoided

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g0pE_taskd.txt vs g1pA_taskb.txt

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g0pE_taskd.txt vs g1pB_taskb.txt

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g0pE_taskd.txt vs g4pE_taskd.txt

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g0pE_taskd.txt vs g2pC_taska.txt

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g0pE_taskd.txt vs g2pC_taskc.txt

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g0pE_taskd.txt vs g2pE_taska.txt

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g0pE_taskd.txt vs orig_taske.txt

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g0pE_taskd.txt vs g0pB_taskc.txt

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

The vector space model has the following limitations:

g0pE_taskd.txt vs g0pC_taskd.txt

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g0pE_taskd.txt vs g0pC_taske.txt

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g0pE_taskd.txt vs g0pD_taskc.txt

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g0pE_taskd.txt vs g0pC_taskb.txt

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g0pE_taskd.txt vs g2pE_taske.txt

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g0pE_taskd.txt vs g0pC_taska.txt

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g0pE_taskd.txt vs g0pD_taska.txt

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g0pE_taskd.txt vs g4pC_taska.txt

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g0pE_taskd.txt vs g1pB_taskc.txt

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g0pE_taskd.txt vs g1pD_taskc.txt

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g0pE_taskd.txt vs g2pB_taske.txt

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

g0pE_taskd.txt vs g2pE_taskc.txt

Bayes Theorem is an important theorem relating conditional probabilities, it allows us to calculate PROB(A|B) from PROB(B|A). Bayes Theorem is important because it can save us from gathering vast amounts of statistical evidence. The main theory is PROB(A|B) = PROB(B|A) * PROB(A) /PROB(B), it means Using PROB(WIN|RAIN) from earlier, we can find the probability that it rained on a day that Harry won a race.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g1pA_taskb.txt vs g1pB_taskb.txt

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g1pA_taskb.txt vs g4pE_taskd.txt

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g1pA_taskb.txt vs g2pC_taska.txt

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g1pA_taskb.txt vs g2pC_taskc.txt

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g1pA_taskb.txt vs g2pE_taska.txt

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g1pA_taskb.txt vs orig_taske.txt

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g1pA_taskb.txt vs g0pB_taskc.txt

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

The vector space model has the following limitations:

g1pA_taskb.txt vs g0pC_taskd.txt

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g1pA_taskb.txt vs g0pC_taske.txt

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g1pA_taskb.txt vs g0pD_taskc.txt

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g1pA_taskb.txt vs g0pC_taskb.txt

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g1pA_taskb.txt vs g2pE_taske.txt

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g1pA_taskb.txt vs g0pC_taska.txt

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g1pA_taskb.txt vs g0pD_taska.txt

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g1pA_taskb.txt vs g4pC_taska.txt

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g1pA_taskb.txt vs g1pB_taskc.txt

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g1pA_taskb.txt vs g1pD_taskc.txt

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g1pA_taskb.txt vs g2pB_taske.txt

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

g1pA_taskb.txt vs g2pE_taskc.txt

The PageRank algorithm is used to designate every aspect of a set of hyperlinked documents with a numerical weighting. It is used by the Google search engine to estimate the relative importance of a web page according to this weighting. The system uses probability distribution to determine the odds that a person randomly clicking on links will arrive at any given page. Following this, each web page is given a ranking of 0-10 according to its relevance to a search. The PageRank is calculated by taking into consideration the number of inbound links, and the PageRank of the pages supplying these links. This means therefore that if a webpage is linked to others that have a high ranking, then it too will receive a high rank. 

Due to the nature of the PageRank system, it is susceptible to manipulation and has been exploited so that certain pages are given a false, exaggerated ranking. In these cases, only Goggle has access to the genuine PageRank. However, much research has been conducted into methods of avoiding links from documents with a false PageRank to try and iron out the bugs in this system and from 2007 Google has actively penalized schemes which try to increase rankings artificially.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g1pB_taskb.txt vs g4pE_taskd.txt

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g1pB_taskb.txt vs g2pC_taska.txt

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g1pB_taskb.txt vs g2pC_taskc.txt

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g1pB_taskb.txt vs g2pE_taska.txt

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g1pB_taskb.txt vs orig_taske.txt

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g1pB_taskb.txt vs g0pB_taskc.txt

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

The vector space model has the following limitations:

g1pB_taskb.txt vs g0pC_taskd.txt

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g1pB_taskb.txt vs g0pC_taske.txt

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g1pB_taskb.txt vs g0pD_taskc.txt

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g1pB_taskb.txt vs g0pC_taskb.txt

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g1pB_taskb.txt vs g2pE_taske.txt

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g1pB_taskb.txt vs g0pC_taska.txt

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g1pB_taskb.txt vs g0pD_taska.txt

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g1pB_taskb.txt vs g4pC_taska.txt

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g1pB_taskb.txt vs g1pB_taskc.txt

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g1pB_taskb.txt vs g1pD_taskc.txt

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g1pB_taskb.txt vs g2pB_taske.txt

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

g1pB_taskb.txt vs g2pE_taskc.txt

A website�s page rank, is how �important� it is on the web.  It is essentially a popularity meter.  Popularity or importance is determined by the amount of links relating to the page there are, there are four different types.  Inbound, links from other pages to yours.  Outbound, links from your page to others.  Dangling, links to a page which has no links to others.  Deep, links to a specific page, usually bypassing the homepage.  The page rank algorithm takes the probability of a �random surfer� becoming bored and requesting another �random page� (otherwise known as the dampening factor) away from 1 and divides this number by the number of pages in the system, adding it to the dampening factor multiplied by the page rank of a linked page divided by the number of outbound links on that linked page.  Adding on this last section for every other page linked to from the original page.  Google uses this algorithm to assist intentional surfers in finding the best websites to suit their needs.  One of the problems with this popularity algorithm is that it is easily manipulated and can give false values, hence the frequent recalculating of page ranks.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g4pE_taskd.txt vs g2pC_taska.txt

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g4pE_taskd.txt vs g2pC_taskc.txt

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g4pE_taskd.txt vs g2pE_taska.txt

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g4pE_taskd.txt vs orig_taske.txt

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g4pE_taskd.txt vs g0pB_taskc.txt

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

The vector space model has the following limitations:

g4pE_taskd.txt vs g0pC_taskd.txt

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g4pE_taskd.txt vs g0pC_taske.txt

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g4pE_taskd.txt vs g0pD_taskc.txt

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g4pE_taskd.txt vs g0pC_taskb.txt

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g4pE_taskd.txt vs g2pE_taske.txt

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g4pE_taskd.txt vs g0pC_taska.txt

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g4pE_taskd.txt vs g0pD_taska.txt

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g4pE_taskd.txt vs g4pC_taska.txt

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g4pE_taskd.txt vs g1pB_taskc.txt

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g4pE_taskd.txt vs g1pD_taskc.txt

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g4pE_taskd.txt vs g2pB_taske.txt

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

g4pE_taskd.txt vs g2pE_taskc.txt

"Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning
The Bayesian Conspiracy is a multinational, interdisciplinary, and shadowy group of scientists that controls publication, grants, tenure, and the illicit traffic in grad students.  The best way to be accepted into the Bayesian Conspiracy is to join the Campus Crusade for Bayes in high school or college, and gradually work your way up to the inner circles. . 
Bayes' Theorem
  	 

Let  and  be sets. Conditional probability requires that 
 	(1) 
where  denotes intersection ("and"), and also that 
 	(2) 
Therefore, 
 	(3) 
Now, let 
 	(4) 
so  is an event in  and  for  , then 
 	(5) 
 	(6) 
But this can be written 
 	(7) 
so 
 


This paper proposes a new measure called scaled inverse document frequency (SIDF) which evaluates the conditional specificity of query terms over a subset S of D and without making any assumption about term independence. S can be estimated from search results, OR searches, or computed from inverted index data. We have evaluated SIDF values from commercial search engines by submitting queries relevant to the financial investment domain. Results compare favorably across search engines and queries. Our approach has practical applications for `real-world� scenarios like in Web Mining, Homeland Security, and keyword-driven marketing research scenarios.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g2pC_taska.txt vs g2pC_taskc.txt

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g2pC_taska.txt vs g2pE_taska.txt

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g2pC_taska.txt vs orig_taske.txt

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g2pC_taska.txt vs g0pB_taskc.txt

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

The vector space model has the following limitations:

g2pC_taska.txt vs g0pC_taskd.txt

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g2pC_taska.txt vs g0pC_taske.txt

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g2pC_taska.txt vs g0pD_taskc.txt

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g2pC_taska.txt vs g0pC_taskb.txt

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g2pC_taska.txt vs g2pE_taske.txt

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g2pC_taska.txt vs g0pC_taska.txt

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g2pC_taska.txt vs g0pD_taska.txt

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g2pC_taska.txt vs g4pC_taska.txt

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g2pC_taska.txt vs g1pB_taskc.txt

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g2pC_taska.txt vs g1pD_taskc.txt

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g2pC_taska.txt vs g2pB_taske.txt

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

g2pC_taska.txt vs g2pE_taskc.txt

Inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.

Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.

In defining this inheritance hierarchy we have already defined certain restrictions, not all of which are desirable. Singleness: using single inheritance, a subclass can inherit from only one superclass. Visibility: whenever client code has access to an object, it generally has access to all the object's superclass data. Static: the inheritance hierarchy of an object is fixed at instantiation when the object's type is selected and does not change with time.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g2pC_taskc.txt vs g2pE_taska.txt

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g2pC_taskc.txt vs orig_taske.txt

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g2pC_taskc.txt vs g0pB_taskc.txt

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

The vector space model has the following limitations:

g2pC_taskc.txt vs g0pC_taskd.txt

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g2pC_taskc.txt vs g0pC_taske.txt

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g2pC_taskc.txt vs g0pD_taskc.txt

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g2pC_taskc.txt vs g0pC_taskb.txt

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g2pC_taskc.txt vs g2pE_taske.txt

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g2pC_taskc.txt vs g0pC_taska.txt

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g2pC_taskc.txt vs g0pD_taska.txt

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g2pC_taskc.txt vs g4pC_taska.txt

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g2pC_taskc.txt vs g1pB_taskc.txt

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g2pC_taskc.txt vs g1pD_taskc.txt

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g2pC_taskc.txt vs g2pB_taske.txt

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

g2pC_taskc.txt vs g2pE_taskc.txt

In the vector space model (VSM), documents take the form of "bags of words" - a standard information retrieval approach which represents documents as in a mathematical "bag" structure, recording what terms are present and how often they occur. 

The vector space model is used in information retrieval to determine how similar documents are to one another, and how similar documents are to a search query. 

In a collection of documents, each document can be viewed as a vector of n values (the terms in the document), where each term is an axis. Queries can also be represented as vectors on this vector space model, and so deciding which document matches the query the closest becomes a matter of selecting the document vector which is nearest to the query vector. 

The query vector is compared to each document vector in turn using a "vector similarity measure", which is the cosine of the angle between the query vector and the document vector. 

This equation is calculated by dividing the dot product of the query vector and the document vector by the modulus of the query vector multiplied by the modulus of the document vector. The denominator takes into account differences in the length of the vector, and has the effect of "normalising" the length. Whichever document returns the highest cosine similarity score is considered to be the closest matching document to the query.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g2pE_taska.txt vs orig_taske.txt

g2pE_taska.txt vs g0pB_taskc.txt

The vector space model has the following limitations:

g2pE_taska.txt vs g0pC_taskd.txt

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g2pE_taska.txt vs g0pC_taske.txt

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g2pE_taska.txt vs g0pD_taskc.txt

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g2pE_taska.txt vs g0pC_taskb.txt

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g2pE_taska.txt vs g2pE_taske.txt

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g2pE_taska.txt vs g0pC_taska.txt

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g2pE_taska.txt vs g0pD_taska.txt

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g2pE_taska.txt vs g4pC_taska.txt

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g2pE_taska.txt vs g1pB_taskc.txt

g2pE_taska.txt vs g1pD_taskc.txt

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g2pE_taska.txt vs g2pB_taske.txt

g2pE_taska.txt vs g2pE_taskc.txt

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

orig_taske.txt vs g0pB_taskc.txt

The vector space model has the following limitations:

orig_taske.txt vs g0pC_taskd.txt

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

orig_taske.txt vs g0pC_taske.txt

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

orig_taske.txt vs g0pD_taskc.txt

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

orig_taske.txt vs g0pC_taskb.txt

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

orig_taske.txt vs g2pE_taske.txt

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

orig_taske.txt vs g0pC_taska.txt

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

orig_taske.txt vs g0pD_taska.txt

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

orig_taske.txt vs g4pC_taska.txt

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

orig_taske.txt vs g1pB_taskc.txt

orig_taske.txt vs g1pD_taskc.txt

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

orig_taske.txt vs g2pB_taske.txt

orig_taske.txt vs g2pE_taskc.txt

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g0pB_taskc.txt vs g0pC_taskd.txt

The vector space model has the following limitations:

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g0pB_taskc.txt vs g0pC_taske.txt

The vector space model has the following limitations:

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g0pB_taskc.txt vs g0pD_taskc.txt

The vector space model has the following limitations:

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g0pB_taskc.txt vs g0pC_taskb.txt

The vector space model has the following limitations:

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g0pB_taskc.txt vs g2pE_taske.txt

The vector space model has the following limitations:

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g0pB_taskc.txt vs g0pC_taska.txt

The vector space model has the following limitations:

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g0pB_taskc.txt vs g0pD_taska.txt

The vector space model has the following limitations:

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g0pB_taskc.txt vs g4pC_taska.txt

The vector space model has the following limitations:

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g0pB_taskc.txt vs g1pB_taskc.txt

The vector space model has the following limitations:

g0pB_taskc.txt vs g1pD_taskc.txt

The vector space model has the following limitations:

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g0pB_taskc.txt vs g2pB_taske.txt

The vector space model has the following limitations:

g0pB_taskc.txt vs g2pE_taskc.txt

The vector space model has the following limitations:

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g0pC_taskd.txt vs g0pC_taske.txt

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g0pC_taskd.txt vs g0pD_taskc.txt

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g0pC_taskd.txt vs g0pC_taskb.txt

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g0pC_taskd.txt vs g2pE_taske.txt

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g0pC_taskd.txt vs g0pC_taska.txt

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g0pC_taskd.txt vs g0pD_taska.txt

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g0pC_taskd.txt vs g4pC_taska.txt

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g0pC_taskd.txt vs g1pB_taskc.txt

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g0pC_taskd.txt vs g1pD_taskc.txt

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g0pC_taskd.txt vs g2pB_taske.txt

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

g0pC_taskd.txt vs g2pE_taskc.txt

In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g0pC_taske.txt vs g0pD_taskc.txt

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g0pC_taske.txt vs g0pC_taskb.txt

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g0pC_taske.txt vs g2pE_taske.txt

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g0pC_taske.txt vs g0pC_taska.txt

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g0pC_taske.txt vs g0pD_taska.txt

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g0pC_taske.txt vs g4pC_taska.txt

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g0pC_taske.txt vs g1pB_taskc.txt

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g0pC_taske.txt vs g1pD_taskc.txt

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g0pC_taske.txt vs g2pB_taske.txt

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

g0pC_taske.txt vs g2pE_taskc.txt

In computer science; dynamic programming is a way of solving problems consist of overlapping subproblems and optimal substructure. The method is more effiecent than naive methods.

The term was first coined in the 1940s by Richard Bellman to describe the process of solving problems where you need to find the best decisions consecutavly. In 1953 he had refined this to the modern meaning. The field was founded as a systems analysis and engineering topic that is recognized by the IEEE. Bellman equation is a central result of dynamic programming which restates an optimization problem in recursive form.

dynamic programming has little connection to computer programming at all, and instead comes from the term mathematical programming, a synonym for optimization. Thus, the program is the best plan for action that is produced. For instance, a events schedule at an exhibition is sometimes called a program. Programming means finding a plan of action.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g0pD_taskc.txt vs g0pC_taskb.txt

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g0pD_taskc.txt vs g2pE_taske.txt

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g0pD_taskc.txt vs g0pC_taska.txt

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g0pD_taskc.txt vs g0pD_taska.txt

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g0pD_taskc.txt vs g4pC_taska.txt

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g0pD_taskc.txt vs g1pB_taskc.txt

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g0pD_taskc.txt vs g1pD_taskc.txt

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g0pD_taskc.txt vs g2pB_taske.txt

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

g0pD_taskc.txt vs g2pE_taskc.txt

An algebraic model for representing text documents and any objects in general is known by the name Vector space model. It represents these as vectors of identifiers, index terms are one illustration of these. The Vector Space model was first used in the SMART Information Retrieval System, and it is utilised variously in indexing, information filtering, indexing and information retrieval.

A document has representation as a vector. Every dimension is precisely related to a separate term. The way in which term is defined depends entirely on the application: typically ‘terms’ are either single words, keywords or longer phrases. The dimensionality of the vector is the number of words in the vocabulary, if it is the words that are chose to be the terms. So the same rule applies with keywords and indeed longer phrases.

If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, additionally known as (term) weights, have been developed. One of the most famous schemes is tf-idf weighting.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g0pC_taskb.txt vs g2pE_taske.txt

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g0pC_taskb.txt vs g0pC_taska.txt

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g0pC_taskb.txt vs g0pD_taska.txt

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g0pC_taskb.txt vs g4pC_taska.txt

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g0pC_taskb.txt vs g1pB_taskc.txt

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g0pC_taskb.txt vs g1pD_taskc.txt

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g0pC_taskb.txt vs g2pB_taske.txt

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

g0pC_taskb.txt vs g2pE_taskc.txt

There are many attributes which infulance the ranking of a page in google, The main too are the content, key words, and links. The content of a webpage generaly gives a good idea about what the page is about, however, there are some flaws in this, for example, for along time ibm web page didnt contain the word computer dispite it being strongly associated with them. To solve this problem, web pages can assign itself key words, which contribute to its ranking in searches.

The second method is the use of links. the more sights which links to your web page and the higher the rank of those sights, the higher the rank of your site will be. This method is used as links are seen as an adoursment of a sight.

With both these methods of ranking web pages, there are issues. key words can be compromised by sparming, google solves this problem by penolizing such activity. Useing links to rank a page also has its problems, for example, link farms which have recursive links, for the sole perpos of raising there ranking, google takels this by useing a dampaning algorthem.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g2pE_taske.txt vs g0pC_taska.txt

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g2pE_taske.txt vs g0pD_taska.txt

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g2pE_taske.txt vs g4pC_taska.txt

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g2pE_taske.txt vs g1pB_taskc.txt

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g2pE_taske.txt vs g1pD_taskc.txt

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g2pE_taske.txt vs g2pB_taske.txt

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

g2pE_taske.txt vs g2pE_taskc.txt

Dynamic Programming (DP) is in basic terms an algorithm design technique that is used for optimization problems and often involves minimizing or maximizing. 
Furthermore, by combining solutions to subproblems, DP solves problems. Subproblems may include and contain many other subsubproblems and even in such cases, the solution to one subproblem may not affect the solutions to other subproblems involved in the same problem. 
By solving subproblems in a bottom-up fashion, which is basically when storing solution to a subproblem the first time it is solved and looking up to find the solution when a subproblem is come across once more,  this would cause DP to reduce computations.  
The following is a generalization path to be taken in Dynamic Programming:
Firstly it is needed to Characterize the structure of an optimal solution. Secondly to define the value of the optimal solution recursively. Furthermore, to compute the optimal solution values either by following a top-down method with caching, or a bottom-up method in a table. The last point would be to construct an optimal solution from the computed values.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g0pC_taska.txt vs g0pD_taska.txt

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g0pC_taska.txt vs g4pC_taska.txt

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g0pC_taska.txt vs g1pB_taskc.txt

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g0pC_taska.txt vs g1pD_taskc.txt

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g0pC_taska.txt vs g2pB_taske.txt

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

g0pC_taska.txt vs g2pE_taskc.txt

inheritance in object oriented programming is where a new class is formed using classes which have allready been defined. These classes have have some of the behavior and attributes which where existent in the classes that it inherited from. The peropos of inheritance in object oriented programming is to minimize the reuse of existing code without modification.

Inheritance allowes classes to be categorized, similer to the way humans catagorize. It also provides a way to generalize du to the "is a" relationship between classes. For example a "cow" is a generalization of "animal" similarly so are "pigs" & cheaters". Defeining classes in this way, allows us to define attributes and behaviours which are commen to all animals in one class, so cheaters would natuarly inheart properities commen to all animals.

The advantage of inheritance is that classes which would otherwise have alot of similar code , can instead shair the same code, thus reducing the complexity of the program. Inheritance, therefore, can also be refered to as polymorphism which is where many pieces of code are controled by shared control code.

Inheritance can be accomplished by overriding methods in its ancestor, or by adding new methods.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g0pD_taska.txt vs g4pC_taska.txt

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g0pD_taska.txt vs g1pB_taskc.txt

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g0pD_taska.txt vs g1pD_taskc.txt

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g0pD_taska.txt vs g2pB_taske.txt

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

g0pD_taska.txt vs g2pE_taskc.txt

Inheritance in object oriented programming is a way to form new classes using classes that have already been defined. The new classes, known as derived classes, inherit attributes and behaviour of the existing classes, which are referred to as base classes. With little or no modification, it is intended to help reuse existing code. It is typically accomplished either by overriding one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor

Inheritance is also sometimes called generalization, because there is-a relationships represent a hierarchy between classes of objects. A ‘fruit’, for instance, is a generalization of "orange", "mango", "apples" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Since apples are fruit (i.e., an apple is-a fruit), conversely apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.

An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code reducing the complexity of the program.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g4pC_taska.txt vs g1pB_taskc.txt

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g4pC_taska.txt vs g1pD_taskc.txt

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g4pC_taska.txt vs g2pB_taske.txt

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

g4pC_taska.txt vs g2pE_taskc.txt

In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula
Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
An advantage of inheritance is that modules with sufficiently similar interfaces can share a lot of code, reducing the complexity of the program. Inheritance therefore has another view, a dual, called polymorphism, which describes many pieces of code being controlled by shared control code.
Inheritance is typically accomplished either by overriding (replacing) one or more methods exposed by ancestor, or by adding new methods to those exposed by an ancestor.
Complex inheritance, or inheritance used within a design that is not sufficiently mature, may lead to the Yo-yo problem.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g1pB_taskc.txt vs g1pD_taskc.txt

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g1pB_taskc.txt vs g2pB_taske.txt

g1pB_taskc.txt vs g2pE_taskc.txt

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g1pD_taskc.txt vs g2pB_taske.txt

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

g1pD_taskc.txt vs g2pE_taskc.txt

Within Information Retrieval each document in a set can be represented as a point in high-dimensional vector space, this representation is called the vector space model. Information Retrieval queries are also represented as vectors in the same vector space; these are then used in conjunction with the document vectors to find relevant documents. The two vectors are compared and the documents with a higher document-query similarity are ranked higher in terms of relevance. There are a variety of techniques that can be used to compare the two vectors; the most frequently used method for the vector space model is the Cosine Coefficient, which calculates the angle between the two vectors and produces a value between 0 and 1.

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.

g2pB_taske.txt vs g2pE_taskc.txt

nformation retrieval (IR) is the science of searching for documents, for information within documents and for metadata about documents, as well as that of searching relational databases and the World Wide Web. IR is interdisciplinary, based on computer science, mathematics, library science, information science, information architecture, cognitive psychology, linguistics, statistics and physics. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis and technologies. 
Automated information retrieval systems are used to reduce what has been called "information overload". Many universities and public libraries use IR systems to provide access to books, journals and other documents.